/* This code can be loaded, or copied and pasted, into Magma. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. At the *bottom* of the file, there is code to recreate the Hilbert modular form in Magma, by creating the HMF space and cutting out the corresponding Hecke irreducible subspace. From there, you can ask for more eigenvalues or modify as desired. It is commented out, as this computation may be lengthy. */ P := PolynomialRing(Rationals()); g := P![-15, 0, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [2, 2, w + 1], [3, 3, w], [5, 5, w], [7, 7, w + 1], [7, 7, w + 6], [11, 11, -w - 2], [11, 11, w - 2], [17, 17, w + 7], [17, 17, w + 10], [43, 43, w + 12], [43, 43, w + 31], [53, 53, w + 11], [53, 53, w + 42], [59, 59, 2*w - 1], [59, 59, -2*w - 1], [61, 61, 2*w - 11], [61, 61, -2*w - 11], [67, 67, w + 22], [67, 67, w + 45], [71, 71, 3*w - 8], [71, 71, -3*w - 8], [103, 103, w + 18], [103, 103, w + 85], [109, 109, 2*w - 13], [109, 109, -2*w - 13], [113, 113, w + 44], [113, 113, w + 69], [127, 127, w + 53], [127, 127, w + 74], [131, 131, 3*w - 2], [131, 131, -3*w - 2], [137, 137, w + 17], [137, 137, w + 120], [163, 163, w + 34], [163, 163, w + 129], [169, 13, -13], [173, 173, w + 19], [173, 173, w + 154], [179, 179, 5*w - 14], [179, 179, -5*w - 14], [181, 181, -w - 14], [181, 181, w - 14], [191, 191, 4*w - 7], [191, 191, -4*w - 7], [197, 197, w + 58], [197, 197, w + 139], [223, 223, w + 98], [223, 223, w + 125], [229, 229, 2*w - 17], [229, 229, -2*w - 17], [233, 233, w + 99], [233, 233, w + 134], [239, 239, -4*w - 1], [239, 239, 4*w - 1], [241, 241, -w - 16], [241, 241, w - 16], [251, 251, 6*w - 17], [251, 251, -6*w - 17], [257, 257, w + 23], [257, 257, w + 234], [283, 283, w + 79], [283, 283, w + 204], [293, 293, w + 111], [293, 293, w + 182], [307, 307, w + 130], [307, 307, w + 177], [311, 311, -5*w - 8], [311, 311, 5*w - 8], [317, 317, w + 40], [317, 317, w + 277], [349, 349, 3*w - 22], [349, 349, -3*w - 22], [353, 353, w + 108], [353, 353, w + 245], [359, 359, 5*w - 4], [359, 359, -5*w - 4], [361, 19, -19], [367, 367, w + 105], [367, 367, w + 262], [409, 409, 5*w - 28], [409, 409, -5*w - 28], [419, 419, 6*w - 11], [419, 419, -6*w - 11], [421, 421, 6*w - 31], [421, 421, -6*w - 31], [431, 431, 8*w - 23], [431, 431, -8*w - 23], [463, 463, w + 101], [463, 463, w + 362], [479, 479, 7*w - 16], [479, 479, -7*w - 16], [487, 487, w + 224], [487, 487, w + 263], [491, 491, -6*w - 7], [491, 491, 6*w - 7], [523, 523, w + 231], [523, 523, w + 292], [529, 23, -23], [541, 541, -3*w - 26], [541, 541, 3*w - 26], [547, 547, w + 62], [547, 547, w + 485], [557, 557, w + 153], [557, 557, w + 404], [593, 593, w + 269], [593, 593, w + 324], [599, 599, -8*w - 19], [599, 599, 8*w - 19], [601, 601, 4*w - 29], [601, 601, -4*w - 29], [607, 607, w + 135], [607, 607, w + 472], [617, 617, w + 218], [617, 617, w + 399], [643, 643, w + 119], [643, 643, w + 524], [653, 653, w + 253], [653, 653, w + 400], [659, 659, 10*w - 29], [659, 659, -10*w - 29], [661, 661, -w - 26], [661, 661, w - 26], [677, 677, w + 37], [677, 677, w + 640], [709, 709, -7*w - 38], [709, 709, 7*w - 38], [719, 719, -7*w - 4], [719, 719, 7*w - 4], [727, 727, w + 200], [727, 727, w + 527], [769, 769, -w - 28], [769, 769, w - 28], [773, 773, w + 244], [773, 773, w + 529], [787, 787, w + 184], [787, 787, w + 603], [797, 797, w + 183], [797, 797, w + 614], [823, 823, w + 76], [823, 823, w + 747], [829, 829, 6*w - 37], [829, 829, -6*w - 37], [839, 839, -8*w - 11], [839, 839, 8*w - 11], [841, 29, -29], [857, 857, w + 300], [857, 857, w + 557], [883, 883, w + 402], [883, 883, w + 481], [907, 907, w + 165], [907, 907, w + 742], [911, 911, 8*w - 7], [911, 911, -8*w - 7], [953, 953, w + 341], [953, 953, w + 612], [961, 31, -31], [967, 967, w + 54], [967, 967, w + 913], [971, 971, 10*w - 23], [971, 971, -10*w - 23], [977, 977, w + 70], [977, 977, w + 907], [1009, 1009, -w - 32], [1009, 1009, w - 32], [1013, 1013, w + 415], [1013, 1013, w + 598], [1019, 1019, -9*w - 14], [1019, 1019, 9*w - 14], [1021, 1021, 3*w - 34], [1021, 1021, -3*w - 34], [1031, 1031, -11*w - 28], [1031, 1031, 11*w - 28], [1063, 1063, w + 503], [1063, 1063, w + 560], [1069, 1069, 5*w - 38], [1069, 1069, -5*w - 38], [1087, 1087, w + 333], [1087, 1087, w + 754], [1091, 1091, 13*w - 38], [1091, 1091, -13*w - 38], [1097, 1097, w + 47], [1097, 1097, w + 1050], [1123, 1123, w + 517], [1123, 1123, w + 606], [1129, 1129, 4*w - 37], [1129, 1129, -4*w - 37], [1151, 1151, 9*w - 8], [1151, 1151, -9*w - 8], [1193, 1193, w + 49], [1193, 1193, w + 1144], [1201, 1201, -7*w - 44], [1201, 1201, 7*w - 44], [1217, 1217, w + 254], [1217, 1217, w + 963], [1249, 1249, -8*w - 47], [1249, 1249, 8*w - 47], [1259, 1259, 14*w - 41], [1259, 1259, -14*w - 41], [1277, 1277, w + 80], [1277, 1277, w + 1197], [1303, 1303, w + 620], [1303, 1303, w + 683], [1319, 1319, -12*w - 29], [1319, 1319, 12*w - 29], [1321, 1321, 11*w - 56], [1321, 1321, -11*w - 56], [1327, 1327, w + 544], [1327, 1327, w + 783], [1369, 37, -37], [1373, 1373, w + 580], [1373, 1373, w + 793], [1381, 1381, 7*w - 46], [1381, 1381, -7*w - 46], [1423, 1423, w + 381], [1423, 1423, w + 1042], [1429, 1429, -w - 38], [1429, 1429, w - 38], [1433, 1433, w + 674], [1433, 1433, w + 759], [1439, 1439, 15*w - 44], [1439, 1439, -15*w - 44], [1447, 1447, w + 66], [1447, 1447, w + 1381], [1451, 1451, -10*w - 7], [1451, 1451, 10*w - 7], [1483, 1483, w + 434], [1483, 1483, w + 1049], [1489, 1489, 9*w - 52], [1489, 1489, -9*w - 52], [1493, 1493, w + 222], [1493, 1493, w + 1271], [1499, 1499, -10*w - 1], [1499, 1499, 10*w - 1], [1511, 1511, 13*w - 32], [1511, 1511, -13*w - 32], [1543, 1543, w + 104], [1543, 1543, w + 1439], [1549, 1549, 11*w - 58], [1549, 1549, -11*w - 58], [1553, 1553, w + 633], [1553, 1553, w + 920], [1559, 1559, 11*w - 16], [1559, 1559, -11*w - 16], [1567, 1567, w + 749], [1567, 1567, w + 818], [1571, 1571, 14*w - 37], [1571, 1571, -14*w - 37], [1609, 1609, -4*w - 43], [1609, 1609, 4*w - 43], [1613, 1613, w + 593], [1613, 1613, w + 1020], [1619, 1619, -11*w - 14], [1619, 1619, 11*w - 14], [1621, 1621, 2*w - 41], [1621, 1621, -2*w - 41], [1627, 1627, w + 760], [1627, 1627, w + 867], [1637, 1637, w + 735], [1637, 1637, w + 902], [1663, 1663, w + 443], [1663, 1663, w + 1220], [1669, 1669, -6*w - 47], [1669, 1669, 6*w - 47], [1681, 41, -41], [1697, 1697, w + 267], [1697, 1697, w + 1430], [1723, 1723, w + 72], [1723, 1723, w + 1651], [1733, 1733, w + 59], [1733, 1733, w + 1674], [1741, 1741, 5*w - 46], [1741, 1741, -5*w - 46], [1747, 1747, w + 310], [1747, 1747, w + 1437], [1783, 1783, w + 753], [1783, 1783, w + 1030], [1789, 1789, 2*w - 43], [1789, 1789, -2*w - 43], [1801, 1801, -3*w - 44], [1801, 1801, 3*w - 44], [1811, 1811, 11*w - 2], [1811, 1811, -11*w - 2], [1861, 1861, 6*w - 49], [1861, 1861, -6*w - 49], [1867, 1867, w + 690], [1867, 1867, w + 1177], [1871, 1871, -12*w - 17], [1871, 1871, 12*w - 17], [1877, 1877, w + 814], [1877, 1877, w + 1063], [1913, 1913, w + 433], [1913, 1913, w + 1480], [1931, 1931, -15*w - 38], [1931, 1931, 15*w - 38], [1973, 1973, w + 691], [1973, 1973, w + 1282], [1979, 1979, -14*w - 31], [1979, 1979, 14*w - 31], [1987, 1987, w + 118], [1987, 1987, w + 1869], [1997, 1997, w + 100], [1997, 1997, w + 1897], [2029, 2029, -11*w - 62], [2029, 2029, 11*w - 62], [2039, 2039, 12*w - 11], [2039, 2039, -12*w - 11], [2083, 2083, w + 981], [2083, 2083, w + 1102], [2089, 2089, -13*w - 68], [2089, 2089, 13*w - 68], [2099, 2099, -14*w - 29], [2099, 2099, 14*w - 29], [2111, 2111, 12*w - 7], [2111, 2111, -12*w - 7], [2143, 2143, w + 882], [2143, 2143, w + 1261], [2153, 2153, w + 605], [2153, 2153, w + 1548], [2161, 2161, 4*w - 49], [2161, 2161, -4*w - 49], [2203, 2203, w + 837], [2203, 2203, w + 1366], [2209, 47, -47], [2213, 2213, w + 194], [2213, 2213, w + 2019], [2221, 2221, 10*w - 61], [2221, 2221, -10*w - 61], [2237, 2237, w + 67], [2237, 2237, w + 2170], [2269, 2269, -6*w - 53], [2269, 2269, 6*w - 53], [2273, 2273, w + 309], [2273, 2273, w + 1964], [2281, 2281, 11*w - 64], [2281, 2281, -11*w - 64], [2287, 2287, w + 483], [2287, 2287, w + 1804], [2297, 2297, w + 974], [2297, 2297, w + 1323], [2333, 2333, w + 919], [2333, 2333, w + 1414], [2339, 2339, -13*w - 14], [2339, 2339, 13*w - 14], [2341, 2341, 2*w - 49], [2341, 2341, -2*w - 49], [2347, 2347, w + 84], [2347, 2347, w + 2263], [2351, 2351, 15*w - 32], [2351, 2351, -15*w - 32], [2357, 2357, w + 1039], [2357, 2357, w + 1318], [2383, 2383, w + 229], [2383, 2383, w + 2154], [2389, 2389, 14*w - 73], [2389, 2389, -14*w - 73], [2393, 2393, w + 761], [2393, 2393, w + 1632], [2399, 2399, 17*w - 44], [2399, 2399, -17*w - 44], [2411, 2411, 14*w - 23], [2411, 2411, -14*w - 23], [2417, 2417, w + 110], [2417, 2417, w + 2307], [2459, 2459, -18*w - 49], [2459, 2459, 18*w - 49], [2467, 2467, w + 233], [2467, 2467, w + 2234], [2477, 2477, w + 510], [2477, 2477, w + 1967], [2503, 2503, w + 1208], [2503, 2503, w + 1295], [2521, 2521, 8*w - 59], [2521, 2521, -8*w - 59], [2531, 2531, 13*w - 2], [2531, 2531, -13*w - 2], [2579, 2579, -14*w - 19], [2579, 2579, 14*w - 19], [2591, 2591, -15*w - 28], [2591, 2591, 15*w - 28], [2633, 2633, w + 1259], [2633, 2633, w + 1374], [2647, 2647, w + 696], [2647, 2647, w + 1951], [2657, 2657, w + 73], [2657, 2657, w + 2584], [2683, 2683, w + 424], [2683, 2683, w + 2259], [2689, 2689, -w - 52], [2689, 2689, w - 52], [2693, 2693, w + 214], [2693, 2693, w + 2479], [2699, 2699, 15*w - 26], [2699, 2699, -15*w - 26], [2707, 2707, w + 285], [2707, 2707, w + 2422], [2711, 2711, 19*w - 52], [2711, 2711, -19*w - 52], [2749, 2749, 2*w - 53], [2749, 2749, -2*w - 53], [2753, 2753, w + 382], [2753, 2753, w + 2371], [2767, 2767, w + 840], [2767, 2767, w + 1927], [2777, 2777, w + 540], [2777, 2777, w + 2237], [2803, 2803, w + 724], [2803, 2803, w + 2079], [2819, 2819, 14*w - 11], [2819, 2819, -14*w - 11], [2837, 2837, w + 306], [2837, 2837, w + 2531], [2879, 2879, 16*w - 31], [2879, 2879, -16*w - 31], [2887, 2887, w + 686], [2887, 2887, w + 2201], [2897, 2897, w + 940], [2897, 2897, w + 1957], [2939, 2939, -14*w - 1], [2939, 2939, 14*w - 1], [2957, 2957, w + 77], [2957, 2957, w + 2880], [2999, 2999, -16*w - 29], [2999, 2999, 16*w - 29], [3001, 3001, -3*w - 56], [3001, 3001, 3*w - 56], [3011, 3011, 18*w - 43], [3011, 3011, -18*w - 43], [3049, 3049, -16*w - 83], [3049, 3049, 16*w - 83], [3061, 3061, 17*w - 86], [3061, 3061, -17*w - 86], [3067, 3067, w + 96], [3067, 3067, w + 2971], [3109, 3109, -7*w - 62], [3109, 3109, 7*w - 62], [3119, 3119, -15*w - 16], [3119, 3119, 15*w - 16], [3121, 3121, -w - 56], [3121, 3121, w - 56], [3137, 3137, w + 363], [3137, 3137, w + 2774], [3163, 3163, w + 1507], [3163, 3163, w + 1656], [3169, 3169, 12*w - 73], [3169, 3169, -12*w - 73], [3181, 3181, 6*w - 61], [3181, 3181, -6*w - 61], [3187, 3187, w + 772], [3187, 3187, w + 2415], [3191, 3191, 20*w - 53], [3191, 3191, -20*w - 53], [3229, 3229, 3*w - 58], [3229, 3229, -3*w - 58], [3251, 3251, -21*w - 58], [3251, 3251, 21*w - 58], [3257, 3257, w + 668], [3257, 3257, w + 2589], [3299, 3299, 19*w - 46], [3299, 3299, -19*w - 46], [3301, 3301, -14*w - 79], [3301, 3301, 14*w - 79], [3307, 3307, w + 315], [3307, 3307, w + 2992], [3343, 3343, w + 689], [3343, 3343, w + 2654], [3359, 3359, -15*w - 4], [3359, 3359, 15*w - 4], [3361, 3361, 7*w - 64], [3361, 3361, -7*w - 64], [3371, 3371, 15*w - 2], [3371, 3371, -15*w - 2], [3413, 3413, w + 1586], [3413, 3413, w + 1827], [3463, 3463, w + 102], [3463, 3463, w + 3361], [3469, 3469, -5*w - 62], [3469, 3469, 5*w - 62], [3491, 3491, -18*w - 37], [3491, 3491, 18*w - 37], [3529, 3529, 8*w - 67], [3529, 3529, -8*w - 67], [3533, 3533, w + 775], [3533, 3533, w + 2758], [3539, 3539, 22*w - 61], [3539, 3539, -22*w - 61], [3541, 3541, 10*w - 71], [3541, 3541, -10*w - 71], [3547, 3547, w + 1235], [3547, 3547, w + 2312], [3557, 3557, w + 634], [3557, 3557, w + 2923], [3583, 3583, w + 1288], [3583, 3583, w + 2295], [3593, 3593, w + 526], [3593, 3593, w + 3067], [3607, 3607, w + 1071], [3607, 3607, w + 2536], [3617, 3617, w + 248], [3617, 3617, w + 3369], [3643, 3643, w + 505], [3643, 3643, w + 3138], [3659, 3659, -17*w - 26], [3659, 3659, 17*w - 26], [3671, 3671, -16*w - 13], [3671, 3671, 16*w - 13], [3677, 3677, w + 393], [3677, 3677, w + 3284], [3709, 3709, -3*w - 62], [3709, 3709, 3*w - 62], [3719, 3719, -16*w - 11], [3719, 3719, 16*w - 11], [3727, 3727, w + 688], [3727, 3727, w + 3039], [3769, 3769, 12*w - 77], [3769, 3769, -12*w - 77], [3779, 3779, -22*w - 59], [3779, 3779, 22*w - 59], [3797, 3797, w + 354], [3797, 3797, w + 3443], [3823, 3823, w + 1329], [3823, 3823, w + 2494], [3833, 3833, w + 1482], [3833, 3833, w + 2351], [3847, 3847, w + 460], [3847, 3847, w + 3387], [3851, 3851, -17*w - 22], [3851, 3851, 17*w - 22], [3889, 3889, 7*w - 68], [3889, 3889, -7*w - 68], [3907, 3907, w + 679], [3907, 3907, w + 3228], [3911, 3911, 21*w - 52], [3911, 3911, -21*w - 52], [3917, 3917, w + 140], [3917, 3917, w + 3777], [3943, 3943, w + 514], [3943, 3943, w + 3429], [3967, 3967, w + 345], [3967, 3967, w + 3622], [4003, 4003, w + 639], [4003, 4003, w + 3364], [4013, 4013, w + 1523], [4013, 4013, w + 2490], [4019, 4019, -18*w - 29], [4019, 4019, 18*w - 29], [4021, 4021, -15*w - 86], [4021, 4021, 15*w - 86], [4027, 4027, w + 979], [4027, 4027, w + 3048], [4073, 4073, w + 1388], [4073, 4073, w + 2685], [4079, 4079, 17*w - 16], [4079, 4079, -17*w - 16], [4091, 4091, 23*w - 62], [4091, 4091, -23*w - 62], [4129, 4129, 17*w - 92], [4129, 4129, -17*w - 92], [4133, 4133, w + 91], [4133, 4133, w + 4042], [4139, 4139, 17*w - 14], [4139, 4139, -17*w - 14], [4157, 4157, w + 1003], [4157, 4157, w + 3154], [4201, 4201, 20*w - 101], [4201, 4201, -20*w - 101], [4211, 4211, 26*w - 77], [4211, 4211, -26*w - 77], [4217, 4217, w + 1495], [4217, 4217, w + 2722], [4243, 4243, w + 545], [4243, 4243, w + 3698], [4253, 4253, w + 1992], [4253, 4253, w + 2261], [4259, 4259, 19*w - 34], [4259, 4259, -19*w - 34], [4261, 4261, -9*w - 74], [4261, 4261, 9*w - 74], [4271, 4271, 17*w - 8], [4271, 4271, -17*w - 8], [4327, 4327, w + 114], [4327, 4327, w + 4213], [4337, 4337, w + 1253], [4337, 4337, w + 3084], [4363, 4363, w + 1291], [4363, 4363, w + 3072], [4373, 4373, w + 1835], [4373, 4373, w + 2538], [4391, 4391, -19*w - 32], [4391, 4391, 19*w - 32], [4397, 4397, w + 2008], [4397, 4397, w + 2389], [4423, 4423, w + 176], [4423, 4423, w + 4247], [4441, 4441, 16*w - 91], [4441, 4441, -16*w - 91], [4447, 4447, w + 1378], [4447, 4447, w + 3069], [4451, 4451, -22*w - 53], [4451, 4451, 22*w - 53], [4457, 4457, w + 1706], [4457, 4457, w + 2751], [4483, 4483, w + 1150], [4483, 4483, w + 3333], [4493, 4493, w + 488], [4493, 4493, w + 4005], [4507, 4507, w + 1443], [4507, 4507, w + 3064], [4517, 4517, w + 884], [4517, 4517, w + 3633], [4549, 4549, -18*w - 97], [4549, 4549, 18*w - 97], [4561, 4561, -9*w - 76], [4561, 4561, 9*w - 76], [4567, 4567, w + 317], [4567, 4567, w + 4250], [4603, 4603, w + 737], [4603, 4603, w + 3866], [4621, 4621, 21*w - 106], [4621, 4621, -21*w - 106], [4637, 4637, w + 1578], [4637, 4637, w + 3059], [4663, 4663, w + 2052], [4663, 4663, w + 2611], [4673, 4673, w + 1070], [4673, 4673, w + 3603], [4679, 4679, 21*w - 44], [4679, 4679, -21*w - 44], [4691, 4691, -18*w - 13], [4691, 4691, 18*w - 13], [4723, 4723, w + 575], [4723, 4723, w + 4148], [4729, 4729, -12*w - 83], [4729, 4729, 12*w - 83], [4733, 4733, w + 2014], [4733, 4733, w + 2719], [4751, 4751, -25*w - 68], [4751, 4751, 25*w - 68], [4783, 4783, w + 1950], [4783, 4783, w + 2833], [4789, 4789, 6*w - 73], [4789, 4789, -6*w - 73], [4793, 4793, w + 2319], [4793, 4793, w + 2474], [4799, 4799, -23*w - 56], [4799, 4799, 23*w - 56], [4801, 4801, -4*w - 71], [4801, 4801, 4*w - 71], [4817, 4817, w + 1304], [4817, 4817, w + 3513], [4861, 4861, 13*w - 86], [4861, 4861, -13*w - 86], [4871, 4871, 28*w - 83], [4871, 4871, -28*w - 83], [4877, 4877, w + 1066], [4877, 4877, w + 3811], [4903, 4903, w + 2027], [4903, 4903, w + 2876], [4909, 4909, -11*w - 82], [4909, 4909, 11*w - 82], [4919, 4919, 24*w - 61], [4919, 4919, -24*w - 61], [4931, 4931, 19*w - 22], [4931, 4931, -19*w - 22], [4937, 4937, w + 720], [4937, 4937, w + 4217], [4969, 4969, -8*w - 77], [4969, 4969, 8*w - 77], [4973, 4973, w + 1398], [4973, 4973, w + 3575], [4987, 4987, w + 2400], [4987, 4987, w + 2587], [5023, 5023, w + 2450], [5023, 5023, w + 2573], [5039, 5039, 20*w - 31], [5039, 5039, -20*w - 31], [5051, 5051, 22*w - 47], [5051, 5051, -22*w - 47], [5099, 5099, -26*w - 71], [5099, 5099, 26*w - 71], [5101, 5101, -5*w - 74], [5101, 5101, 5*w - 74], [5107, 5107, w + 530], [5107, 5107, w + 4577], [5153, 5153, w + 296], [5153, 5153, w + 4857], [5167, 5167, w + 2092], [5167, 5167, w + 3075], [5171, 5171, -21*w - 38], [5171, 5171, 21*w - 38], [5209, 5209, 13*w - 88], [5209, 5209, -13*w - 88], [5227, 5227, w + 1944], [5227, 5227, w + 3283], [5231, 5231, -23*w - 52], [5231, 5231, 23*w - 52], [5237, 5237, w + 1780], [5237, 5237, w + 3457], [5273, 5273, w + 2015], [5273, 5273, w + 3258], [5279, 5279, -25*w - 64], [5279, 5279, 25*w - 64], [5281, 5281, -8*w - 79], [5281, 5281, 8*w - 79], [5297, 5297, w + 103], [5297, 5297, w + 5194], [5323, 5323, w + 2168], [5323, 5323, w + 3155], [5329, 73, -73], [5333, 5333, w + 1173], [5333, 5333, w + 4160], [5347, 5347, w + 343], [5347, 5347, w + 5004], [5351, 5351, 19*w - 8], [5351, 5351, -19*w - 8], [5393, 5393, w + 727], [5393, 5393, w + 4666], [5399, 5399, -19*w - 4], [5399, 5399, 19*w - 4], [5407, 5407, w + 2003], [5407, 5407, w + 3404], [5417, 5417, w + 477], [5417, 5417, w + 4940], [5443, 5443, w + 1613], [5443, 5443, w + 3830], [5449, 5449, 20*w - 107], [5449, 5449, -20*w - 107], [5471, 5471, -20*w - 23], [5471, 5471, 20*w - 23], [5477, 5477, w + 1504], [5477, 5477, w + 3973], [5503, 5503, w + 836], [5503, 5503, w + 4667], [5519, 5519, -28*w - 79], [5519, 5519, 28*w - 79], [5521, 5521, 23*w - 116], [5521, 5521, -23*w - 116], [5527, 5527, w + 2699], [5527, 5527, w + 2828], [5531, 5531, 25*w - 62], [5531, 5531, -25*w - 62], [5563, 5563, w + 2403], [5563, 5563, w + 3160], [5569, 5569, 16*w - 97], [5569, 5569, -16*w - 97], [5573, 5573, w + 2404], [5573, 5573, w + 3169], [5581, 5581, 11*w - 86], [5581, 5581, -11*w - 86], [5591, 5591, -21*w - 32], [5591, 5591, 21*w - 32], [5623, 5623, w + 1356], [5623, 5623, w + 4267], [5639, 5639, 20*w - 19], [5639, 5639, -20*w - 19], [5641, 5641, 3*w - 76], [5641, 5641, -3*w - 76], [5647, 5647, w + 1200], [5647, 5647, w + 4447], [5651, 5651, -26*w - 67], [5651, 5651, 26*w - 67], [5657, 5657, w + 1850], [5657, 5657, w + 3807], [5683, 5683, w + 1163], [5683, 5683, w + 4520], [5689, 5689, 4*w - 77], [5689, 5689, -4*w - 77], [5693, 5693, w + 489], [5693, 5693, w + 5204], [5701, 5701, 6*w - 79], [5701, 5701, -6*w - 79], [5711, 5711, 20*w - 17], [5711, 5711, -20*w - 17], [5717, 5717, w + 107], [5717, 5717, w + 5610], [5743, 5743, w + 2623], [5743, 5743, w + 3120], [5749, 5749, 18*w - 103], [5749, 5749, -18*w - 103], [5813, 5813, w + 438], [5813, 5813, w + 5375], [5821, 5821, 19*w - 106], [5821, 5821, -19*w - 106], [5827, 5827, w + 202], [5827, 5827, w + 5625], [5869, 5869, 2*w - 77], [5869, 5869, -2*w - 77], [5879, 5879, 20*w - 11], [5879, 5879, -20*w - 11], [5881, 5881, 20*w - 109], [5881, 5881, -20*w - 109], [5897, 5897, w + 1395], [5897, 5897, w + 4502], [5923, 5923, w + 361], [5923, 5923, w + 5562], [5939, 5939, 21*w - 26], [5939, 5939, -21*w - 26], [6007, 6007, w + 1358], [6007, 6007, w + 4649], [6011, 6011, 25*w - 58], [6011, 6011, -25*w - 58], [6043, 6043, w + 2083], [6043, 6043, w + 3960], [6053, 6053, w + 2803], [6053, 6053, w + 3250], [6067, 6067, w + 1389], [6067, 6067, w + 4678], [6113, 6113, w + 2969], [6113, 6113, w + 3144], [6121, 6121, -12*w - 91], [6121, 6121, 12*w - 91], [6131, 6131, -21*w - 22], [6131, 6131, 21*w - 22], [6163, 6163, w + 1062], [6163, 6163, w + 5101], [6173, 6173, w + 572], [6173, 6173, w + 5601], [6197, 6197, w + 1262], [6197, 6197, w + 4935], [6229, 6229, 15*w - 98], [6229, 6229, -15*w - 98], [6241, 79, -79], [6247, 6247, w + 2800], [6247, 6247, w + 3447], [6257, 6257, w + 1354], [6257, 6257, w + 4903], [6299, 6299, -22*w - 31], [6299, 6299, 22*w - 31], [6301, 6301, -13*w - 94], [6301, 6301, 13*w - 94], [6311, 6311, -27*w - 68], [6311, 6311, 27*w - 68], [6317, 6317, w + 2068], [6317, 6317, w + 4249], [6343, 6343, w + 138], [6343, 6343, w + 6205], [6353, 6353, w + 1506], [6353, 6353, w + 4847], [6359, 6359, -21*w - 16], [6359, 6359, 21*w - 16], [6361, 6361, -16*w - 101], [6361, 6361, 16*w - 101], [6367, 6367, w + 1231], [6367, 6367, w + 5136], [6421, 6421, -10*w - 89], [6421, 6421, 10*w - 89], [6427, 6427, w + 972], [6427, 6427, w + 5455], [6469, 6469, -14*w - 97], [6469, 6469, 14*w - 97], [6473, 6473, w + 706], [6473, 6473, w + 5767], [6481, 6481, -17*w - 104], [6481, 6481, 17*w - 104], [6491, 6491, 23*w - 38], [6491, 6491, -23*w - 38], [6529, 6529, 9*w - 88], [6529, 6529, -9*w - 88], [6547, 6547, w + 1672], [6547, 6547, w + 4875], [6551, 6551, -21*w - 8], [6551, 6551, 21*w - 8], [6599, 6599, 21*w - 4], [6599, 6599, -21*w - 4], [6607, 6607, w + 3233], [6607, 6607, w + 3374], [6653, 6653, w + 2518], [6653, 6653, w + 4135], [6659, 6659, 26*w - 59], [6659, 6659, -26*w - 59], [6661, 6661, -7*w - 86], [6661, 6661, 7*w - 86], [6703, 6703, w + 685], [6703, 6703, w + 6018], [6709, 6709, -w - 82], [6709, 6709, w - 82], [6719, 6719, 28*w - 71], [6719, 6719, -28*w - 71], [6737, 6737, w + 1092], [6737, 6737, w + 5645], [6763, 6763, w + 2051], [6763, 6763, w + 4712], [6779, 6779, 23*w - 34], [6779, 6779, -23*w - 34], [6781, 6781, 10*w - 91], [6781, 6781, -10*w - 91], [6791, 6791, 24*w - 43], [6791, 6791, -24*w - 43], [6823, 6823, w + 1473], [6823, 6823, w + 5350], [6829, 6829, 2*w - 83], [6829, 6829, -2*w - 83], [6833, 6833, w + 3324], [6833, 6833, w + 3509], [6841, 6841, 21*w - 116], [6841, 6841, -21*w - 116], [6857, 6857, w + 1264], [6857, 6857, w + 5593], [6883, 6883, w + 842], [6883, 6883, w + 6041], [6889, 83, -83], [6899, 6899, -22*w - 19], [6899, 6899, 22*w - 19], [6907, 6907, w + 144], [6907, 6907, w + 6763], [6911, 6911, 23*w - 32], [6911, 6911, -23*w - 32], [6917, 6917, w + 3287], [6917, 6917, w + 3630], [6949, 6949, 23*w - 122], [6949, 6949, -23*w - 122], [6959, 6959, 24*w - 41], [6959, 6959, -24*w - 41], [6961, 6961, 8*w - 89], [6961, 6961, -8*w - 89], [6967, 6967, w + 843], [6967, 6967, w + 6124], [6971, 6971, 22*w - 17], [6971, 6971, -22*w - 17], [6977, 6977, w + 3122], [6977, 6977, w + 3855], [7013, 7013, w + 2298], [7013, 7013, w + 4715], [7019, 7019, 31*w - 86], [7019, 7019, -31*w - 86], [7027, 7027, w + 1134], [7027, 7027, w + 5893], [7069, 7069, 13*w - 98], [7069, 7069, -13*w - 98], [7079, 7079, 32*w - 91], [7079, 7079, -32*w - 91], [7129, 7129, 19*w - 112], [7129, 7129, -19*w - 112], [7151, 7151, 23*w - 28], [7151, 7151, -23*w - 28], [7193, 7193, w + 2461], [7193, 7193, w + 4732], [7207, 7207, w + 465], [7207, 7207, w + 6742], [7211, 7211, 22*w - 7], [7211, 7211, -22*w - 7], [7243, 7243, w + 2852], [7243, 7243, w + 4391], [7253, 7253, w + 2458], [7253, 7253, w + 4795], [7309, 7309, -21*w - 118], [7309, 7309, 21*w - 118], [7321, 7321, 8*w - 91], [7321, 7321, -8*w - 91], [7331, 7331, -26*w - 53], [7331, 7331, 26*w - 53], [7369, 7369, 5*w - 88], [7369, 7369, -5*w - 88], [7433, 7433, w + 2902], [7433, 7433, w + 4531], [7451, 7451, 23*w - 22], [7451, 7451, -23*w - 22], [7457, 7457, w + 1643], [7457, 7457, w + 5814], [7489, 7489, 24*w - 127], [7489, 7489, -24*w - 127], [7499, 7499, -33*w - 94], [7499, 7499, 33*w - 94], [7507, 7507, w + 2744], [7507, 7507, w + 4763], [7517, 7517, w + 1575], [7517, 7517, w + 5942], [7549, 7549, 26*w - 133], [7549, 7549, -26*w - 133], [7559, 7559, 35*w - 104], [7559, 7559, -35*w - 104], [7561, 7561, 27*w - 136], [7561, 7561, -27*w - 136], [7577, 7577, w + 2904], [7577, 7577, w + 4673], [7603, 7603, w + 409], [7603, 7603, w + 7194], [7621, 7621, -9*w - 94], [7621, 7621, 9*w - 94], [7669, 7669, 14*w - 103], [7669, 7669, -14*w - 103], [7673, 7673, w + 1407], [7673, 7673, w + 6266], [7681, 7681, 4*w - 89], [7681, 7681, -4*w - 89], [7687, 7687, w + 232], [7687, 7687, w + 7455], [7691, 7691, -31*w - 82], [7691, 7691, 31*w - 82], [7723, 7723, w + 1969], [7723, 7723, w + 5754], [7741, 7741, 6*w - 91], [7741, 7741, -6*w - 91], [7757, 7757, w + 1746], [7757, 7757, w + 6011], [7789, 7789, -11*w - 98], [7789, 7789, 11*w - 98], [7793, 7793, w + 364], [7793, 7793, w + 7429], [7817, 7817, w + 573], [7817, 7817, w + 7244], [7853, 7853, w + 3337], [7853, 7853, w + 4516], [7867, 7867, w + 2270], [7867, 7867, w + 5597], [7877, 7877, w + 1550], [7877, 7877, w + 6327], [7919, 7919, -23*w - 4], [7919, 7919, 23*w - 4], [7921, 89, -89], [7927, 7927, w + 2394], [7927, 7927, w + 5533], [7937, 7937, w + 1431], [7937, 7937, w + 6506], [7963, 7963, w + 3269], [7963, 7963, w + 4694], [8039, 8039, 28*w - 61], [8039, 8039, -28*w - 61], [8089, 8089, -5*w - 92], [8089, 8089, 5*w - 92], [8093, 8093, w + 3861], [8093, 8093, w + 4232], [8101, 8101, -7*w - 94], [8101, 8101, 7*w - 94], [8111, 8111, 24*w - 23], [8111, 8111, -24*w - 23], [8117, 8117, w + 2487], [8117, 8117, w + 5630], [8161, 8161, -20*w - 119], [8161, 8161, 20*w - 119], [8167, 8167, w + 495], [8167, 8167, w + 7672], [8171, 8171, -30*w - 73], [8171, 8171, 30*w - 73], [8209, 8209, -17*w - 112], [8209, 8209, 17*w - 112], [8219, 8219, 25*w - 34], [8219, 8219, -25*w - 34], [8221, 8221, 2*w - 91], [8221, 8221, -2*w - 91], [8231, 8231, -27*w - 52], [8231, 8231, 27*w - 52], [8237, 8237, w + 930], [8237, 8237, w + 7307], [8263, 8263, w + 2126], [8263, 8263, w + 6137], [8269, 8269, 21*w - 122], [8269, 8269, -21*w - 122], [8273, 8273, w + 2310], [8273, 8273, w + 5963], [8287, 8287, w + 427], [8287, 8287, w + 7860], [8291, 8291, 26*w - 43], [8291, 8291, -26*w - 43], [8297, 8297, w + 1417], [8297, 8297, w + 6880], [8329, 8329, -3*w - 92], [8329, 8329, 3*w - 92], [8389, 8389, -9*w - 98], [8389, 8389, 9*w - 98], [8443, 8443, w + 431], [8443, 8443, w + 8012], [8461, 8461, -5*w - 94], [8461, 8461, 5*w - 94], [8467, 8467, w + 3715], [8467, 8467, w + 4752], [8513, 8513, w + 2794], [8513, 8513, w + 5719], [8521, 8521, 24*w - 131], [8521, 8521, -24*w - 131], [8527, 8527, w + 2303], [8527, 8527, w + 6224], [8537, 8537, w + 2267], [8537, 8537, w + 6270], [8563, 8563, w + 1989], [8563, 8563, w + 6574], [8573, 8573, w + 131], [8573, 8573, w + 8442], [8581, 8581, -25*w - 134], [8581, 8581, 25*w - 134], [8597, 8597, w + 1369], [8597, 8597, w + 7228], [8623, 8623, w + 1757], [8623, 8623, w + 6866], [8629, 8629, -26*w - 137], [8629, 8629, 26*w - 137], [8641, 8641, 20*w - 121], [8641, 8641, -20*w - 121], [8647, 8647, w + 2533], [8647, 8647, w + 6114], [8689, 8689, -28*w - 143], [8689, 8689, 28*w - 143], [8693, 8693, w + 923], [8693, 8693, w + 7770], [8699, 8699, -25*w - 26], [8699, 8699, 25*w - 26], [8707, 8707, w + 4230], [8707, 8707, w + 4477], [8753, 8753, w + 3966], [8753, 8753, w + 4787], [8761, 8761, 21*w - 124], [8761, 8761, -21*w - 124], [8803, 8803, w + 785], [8803, 8803, w + 8018], [8819, 8819, -27*w - 46], [8819, 8819, 27*w - 46], [8821, 8821, -w - 94], [8821, 8821, w - 94], [8831, 8831, -36*w - 103], [8831, 8831, 36*w - 103], [8837, 8837, w + 133], [8837, 8837, w + 8704], [8863, 8863, w + 3355], [8863, 8863, w + 5508], [8887, 8887, w + 3872], [8887, 8887, w + 5015], [8923, 8923, w + 1529], [8923, 8923, w + 7394], [8929, 8929, 16*w - 113], [8929, 8929, -16*w - 113], [8933, 8933, w + 4195], [8933, 8933, w + 4738], [8941, 8941, -14*w - 109], [8941, 8941, 14*w - 109], [8951, 8951, -28*w - 53], [8951, 8951, 28*w - 53], [8999, 8999, -27*w - 44], [8999, 8999, 27*w - 44], [9001, 9001, -11*w - 104], [9001, 9001, 11*w - 104], [9007, 9007, w + 3346], [9007, 9007, w + 5661], [9011, 9011, -30*w - 67], [9011, 9011, 30*w - 67], [9043, 9043, w + 1033], [9043, 9043, w + 8010], [9049, 9049, -24*w - 133], [9049, 9049, 24*w - 133], [9059, 9059, -34*w - 91], [9059, 9059, 34*w - 91], [9067, 9067, w + 1469], [9067, 9067, w + 7598], [9103, 9103, w + 4161], [9103, 9103, w + 4942], [9109, 9109, -10*w - 103], [9109, 9109, 10*w - 103], [9127, 9127, w + 782], [9127, 9127, w + 8345], [9137, 9137, w + 1487], [9137, 9137, w + 7650], [9173, 9173, w + 3545], [9173, 9173, w + 5628], [9181, 9181, 26*w - 139], [9181, 9181, -26*w - 139], [9187, 9187, w + 525], [9187, 9187, w + 8662], [9239, 9239, -36*w - 101], [9239, 9239, 36*w - 101], [9241, 9241, -8*w - 101], [9241, 9241, 8*w - 101], [9257, 9257, w + 2215], [9257, 9257, w + 7042], [9283, 9283, w + 1823], [9283, 9283, w + 7460], [9293, 9293, w + 2675], [9293, 9293, w + 6618], [9311, 9311, 25*w - 8], [9311, 9311, -25*w - 8], [9343, 9343, w + 3029], [9343, 9343, w + 6314], [9349, 9349, 2*w - 97], [9349, 9349, -2*w - 97], [9371, 9371, 25*w - 2], [9371, 9371, -25*w - 2], [9377, 9377, w + 137], [9377, 9377, w + 9240], [9403, 9403, w + 168], [9403, 9403, w + 9235], [9409, 97, -97], [9413, 9413, w + 1265], [9413, 9413, w + 8148], [9419, 9419, -34*w - 89], [9419, 9419, 34*w - 89], [9421, 9421, -11*w - 106], [9421, 9421, 11*w - 106], [9431, 9431, -32*w - 77], [9431, 9431, 32*w - 77], [9437, 9437, w + 1073], [9437, 9437, w + 8364], [9463, 9463, w + 3367], [9463, 9463, w + 6096], [9473, 9473, w + 3817], [9473, 9473, w + 5656], [9479, 9479, -29*w - 56], [9479, 9479, 29*w - 56], [9491, 9491, -27*w - 38], [9491, 9491, 27*w - 38], [9497, 9497, w + 3511], [9497, 9497, w + 5986], [9533, 9533, w + 4117], [9533, 9533, w + 5416], [9539, 9539, 35*w - 94], [9539, 9539, -35*w - 94], [9547, 9547, w + 1712], [9547, 9547, w + 7835], [9551, 9551, -28*w - 47], [9551, 9551, 28*w - 47], [9601, 9601, 9*w - 104], [9601, 9601, -9*w - 104], [9643, 9643, w + 3765], [9643, 9643, w + 5878], [9649, 9649, -8*w - 103], [9649, 9649, 8*w - 103], [9661, 9661, -6*w - 101], [9661, 9661, 6*w - 101], [9677, 9677, w + 220], [9677, 9677, w + 9457], [9719, 9719, 37*w - 104], [9719, 9719, -37*w - 104], [9721, 9721, 12*w - 109], [9721, 9721, -12*w - 109], [9769, 9769, -21*w - 128], [9769, 9769, 21*w - 128], [9781, 9781, 18*w - 121], [9781, 9781, -18*w - 121], [9787, 9787, w + 3175], [9787, 9787, w + 6612], [9791, 9791, 31*w - 68], [9791, 9791, -31*w - 68], [9829, 9829, 14*w - 113], [9829, 9829, -14*w - 113], [9833, 9833, w + 3037], [9833, 9833, w + 6796], [9839, 9839, 40*w - 119], [9839, 9839, -40*w - 119], [9851, 9851, 26*w - 17], [9851, 9851, -26*w - 17], [9857, 9857, w + 4204], [9857, 9857, w + 5653], [9883, 9883, w + 3077], [9883, 9883, w + 6806], [9901, 9901, -22*w - 131], [9901, 9901, 22*w - 131], [9907, 9907, w + 3458], [9907, 9907, w + 6449], [9949, 9949, 10*w - 107], [9949, 9949, -10*w - 107], [9967, 9967, w + 3952], [9967, 9967, w + 6015]]; primes := [ideal : I in primesArray]; heckePol := x; K := Rationals(); e := 1; heckeEigenvaluesArray := [0, -1, -1, -2, 4, -6, 0, 0, 0, 4, 4, 6, 6, -12, -6, 8, -4, 4, -8, 0, -12, -14, 4, -4, -16, -6, 6, 16, -2, 0, 6, -18, 18, -20, -20, 2, -6, -18, -6, 0, -4, 8, -24, 0, 6, -18, -14, -8, -22, 2, 0, 24, -12, 0, 2, 14, 24, -30, -6, 6, -20, 4, 18, -6, 28, 4, 24, -24, -6, 18, -28, 8, -24, 24, 24, -24, -10, -14, 4, 14, 14, -18, -12, -10, -10, 24, 12, 4, 22, 0, 36, -32, -14, -36, -42, -20, 28, 26, -40, 44, 28, -8, -18, 30, -6, -42, 12, 24, 14, 14, 22, 40, 12, 12, -32, 4, -18, 6, 6, 36, -4, -40, -42, -18, 38, -10, 0, -24, -14, 16, -34, 14, 18, -30, -8, 28, 30, -30, 40, -2, -16, -52, 24, 0, 50, -24, 48, 4, -20, -8, 28, 0, -24, -54, -18, 38, -32, -14, 36, 54, 12, -12, 2, -10, -42, -54, -24, 30, 2, -46, 24, 36, -38, -44, 2, 26, -44, 10, 0, -18, -42, -6, 4, 16, -22, -46, 48, 12, 6, 42, -58, 14, -42, 66, -46, 62, 6, 0, 30, -66, -26, 16, -48, -24, -46, 26, 22, -8, 2, 18, -54, 14, 62, 34, -56, -34, -34, 66, -18, 60, -24, 4, 70, 60, -42, 28, -44, -22, -22, -42, 54, 30, 0, 48, 72, -14, -20, -16, -4, -12, 12, -24, 12, -56, 22, 66, 36, 62, -34, 42, 66, -36, 54, -40, -4, 28, 64, 42, 18, -26, 52, -58, 14, -46, 54, 42, 40, 4, -6, -6, -22, 50, -20, -20, -56, 46, -52, -16, -46, 74, 36, 18, -46, 2, 4, 64, 12, 48, 30, 78, -72, -48, -18, 36, -54, 6, 42, -84, -44, 28, 66, -6, 14, 38, -12, 0, 76, -8, -58, 74, -60, -18, 84, -24, 22, 76, 72, 48, -70, -34, 4, 16, 14, -54, -66, 38, 62, 6, 78, 74, -46, -84, 84, -58, -10, 88, -2, 48, 72, -6, -6, -48, -78, 2, 2, 28, 16, -24, 0, -42, -54, 40, 34, -76, 8, 48, 24, 12, 72, 84, -42, -66, 42, -42, 0, 16, 52, 54, 30, -74, -56, 86, 14, 48, -66, 18, 24, 0, 24, -90, -6, 70, -20, -12, 60, -20, 16, -10, -58, 78, 54, -30, -36, -8, 28, -60, 24, -58, -58, 102, 66, 64, -26, -90, -78, -104, -44, 78, -84, 6, -18, -48, 12, -50, -68, -30, 54, -6, 36, 78, 78, -24, 24, -10, 86, -42, 96, 26, -10, -16, 20, -68, -8, 14, 86, -72, 24, -82, -34, -24, 72, 76, 100, -94, 26, -70, 98, 16, 52, 72, -24, 44, -64, -72, -42, -42, -30, 84, -66, 86, -58, 16, -92, -32, 58, -12, -24, 2, -46, -60, -114, -78, 90, -14, 76, 74, 74, -36, -102, -10, -106, 30, 54, -72, 42, -4, -40, -92, 88, 6, -6, -56, 34, -84, -84, 58, -56, 0, 0, -44, 16, -96, 6, 24, 36, -114, -30, 50, -22, 48, -36, -62, -68, -58, 86, -84, 6, -42, 102, -8, -62, 96, 72, 70, -68, -12, 30, 50, -82, -80, -20, 12, 0, 30, 18, 34, 28, -98, -56, 64, -44, -78, -18, 72, -102, -28, 80, 88, -68, 6, 114, -24, 96, -108, 6, 14, 50, 42, 18, -6, -84, 30, 6, 50, -70, 84, -30, 114, 78, -44, -80, 30, -54, -72, -6, 92, 8, 120, 24, -104, 82, 12, 84, 124, 4, 114, -126, -36, 120, -126, -30, 16, 94, 110, 26, -56, -26, -66, -24, -90, 90, -56, 124, 6, 6, 64, -116, 66, -102, -40, 68, 14, 74, -8, 82, 76, 76, -118, -94, -42, 30, -20, 106, -18, 66, -48, 48, 12, 18, -68, 28, -106, -46, -90, -114, -72, -24, -104, 82, 128, 92, -36, -36, 48, -84, -94, 122, 114, -90, 104, -100, 72, -120, -6, 42, -44, 10, -112, -4, -48, 36, -18, 72, 48, 24, -70, 38, 114, 66, -20, 52, -2, -92, -96, 0, -84, -18, -84, 66, 8, -100, 88, -116, -30, 6, -14, -92, -6, -84, -22, 26, 28, 52, -72, -60, 54, 78, -36, -36, -120, 24, -130, -46, 84, 60, 4, 76, 74, 54, -42, 52, -8, -48, -96, 12, -12, -108, 48, -116, -62, -18, 18, 100, -44, -70, -22, -12, 48, 18, -42, 16, -14, 120, -120, 122, -70, 100, -74, -72, 42, -56, -20, -58, 110, 6, -6, 104, -4, 12, 120, 142, -128, 96, -108, -118, 26, 40, 22, -24, -42, -42, -102, 4, -32, -70, -70, -66, -78, -22, 74, -48, 12, -90, 30, -116, -50, -16, 140, -18, -114, 98, 146, 16, 28, 26, -94, -72, -96, 50, -94, 12, -132, -68, 28, 126, 132, 154, 40, 18, 0, 28, 64, -78, -102, -68, 124, -66, 18, 2, 50, -48, -114, -116, 64, -114, 102, 54, 78, -142, 2, -58, 70, 28, -138, -78, 90, 12, -46, 50, -24, -72, 150, -78, 154, -44, 30, -6, -36, 120, -10, 38, -74, 16, 68, 32, -92, -20, 104, 20, -48, 24, 110, 38, -144, -150, 158, 14, -68, 76, 36, 24, -120, 120, -128, -2, 102, -90, 102, 108, 8, -100, -2, -20, -124, -40, -144, 24, -126, 78, -140, 148, 36, -30, 50, -22, -36, 120, 148, 154, 38, 134, -84, -60, -154, -10, -48, -120, -152, 52, 86, -114, 108, 4, 4, -120, 0, 42, -6, 2, -70, 132, -24, 158, -10, -128, -38, -132, -90, -12, 60, 54, -114, 18, -60, 100, 28, -82, -58, -72, -60, 110, 38, 108, 48, -66, -102, -158, -8, 66, -168, -104, 52, 54, 54, 128, -100, 26, -82, -126, 108, 14, -34, -102, -114, 18, 144, -60, 12, -82, -82, 18, 108, -80, -116, 150, 162, 80, -100, -36, 0, -10, -70, 60, -84, 64, -116, -46, -118, 92, 128, -12, 84, -10, 14, -128, -134, -36, -90, 16, -92, -106, -34, -66, 18, 86, 86, -36, -108, 108, -36, -30, 18, 148, 16, 18, -174, -132, -96, -70, 88, -38, -168, -72, 136, 100, 144, 144, 98, 134, -6, 30, -58, 38, -120, 36, -42, 162, -130, 14, -122, -68, -12, 6, -34, -130, 96, -42, 122, -94, 0, -108, -42, 102, 124, 130, -82, -154, -84, 84, 10, 52, -30, 84, 12, -132, -22, -22, 50, 2, -20, 136, 146, 2, 52, -32, -156, -132, -10, 62, 58, 76, -102, -138, 16, 76, 18, 18, -4, -40, 114, -78, 160, -86, -10, -10, 50, 98, -128, 10, -10, -46, 150, 54, 168, 54, 100, -92, 18, -18, -166, 38, -20, 124, -138, 180, 134, -130, -168, 168, 78, 150, -26, -92, -38, -8, 4, -32, 98, 86, 102, -162, 50, -94, -48, 72, 120, -180, -70, -94, -98, 64, 120, 78, 28, 52, 110, 86, -66, 12, 124, 124, -110, 88, 140, -64, -182, -56, -66, -30, 150, -150, -70, -70, -44, -92, 120, 156, 170, -118, -126, -66, -68, 4, -114, 138, -72, 12, 22, 76, 8, 116, -24, 18, 78, -78, -8, -116, 2, -78, -174, 72, 6, -34, -34, -12, -24, -174, 114, -14, -68, 6, 114, 24, -120, 114, -60, 126, -102, 30, 102, 72, 162, -188, 28, -12, 0, 74, 122, 4, -44, 110, -154, -148, 8, 78, -42, -24, -120, 86, -106, -22, -70, 146, -118, 4, 172, -120, 0, -190, 146, -24, 48, 168, 0, 156, 126, 90, -90, 124, -32, 56, -52, 4, 112, -94, 2, -152, -122]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := -1; ALEigenvalues[ideal] := 1; ALEigenvalues[ideal] := 1; // EXAMPLE: // pp := Factorization(2*ZF)[1][1]; // heckeEigenvalues[pp]; print "To reconstruct the Hilbert newform f, type f, iso := Explode(make_newform());"; function make_newform(); M := HilbertCuspForms(F, NN); S := NewSubspace(M); // SetVerbose("ModFrmHil", 1); NFD := NewformDecomposition(S); newforms := [* Eigenform(U) : U in NFD *]; if #newforms eq 0 then; print "No Hilbert newforms at this level"; return 0; end if; print "Testing ", #newforms, " possible newforms"; newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *]; print #newforms, " newforms have the correct Hecke field"; if #newforms eq 0 then; print "No Hilbert newform found with the correct Hecke field"; return 0; end if; autos := Automorphisms(K); xnewforms := [* *]; for f in newforms do; if K eq RationalField() then; Append(~xnewforms, [* f, autos[1] *]); else; flag, iso := IsIsomorphic(K,BaseField(f)); for a in autos do; Append(~xnewforms, [* f, a*iso *]); end for; end if; end for; newforms := xnewforms; for P in primes do; xnewforms := [* *]; for f_iso in newforms do; f, iso := Explode(f_iso); if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then; Append(~xnewforms, f_iso); end if; end for; newforms := xnewforms; if #newforms eq 0 then; print "No Hilbert newform found which matches the Hecke eigenvalues"; return 0; else if #newforms eq 1 then; print "success: unique match"; return newforms[1]; end if; end if; end for; print #newforms, "Hilbert newforms found which match the Hecke eigenvalues"; return newforms[1]; end function;