/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([-36, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, 3]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [3, 3, w],\ [3, 3, w + 2],\ [5, 5, w + 2],\ [17, 17, w + 1],\ [17, 17, w + 15],\ [29, 29, w + 14],\ [37, 37, w + 10],\ [37, 37, w + 26],\ [43, 43, w + 19],\ [43, 43, w + 23],\ [47, 47, w + 22],\ [47, 47, w + 24],\ [49, 7, -7],\ [59, 59, w + 16],\ [59, 59, w + 42],\ [71, 71, w + 21],\ [71, 71, w + 49],\ [73, 73, w + 13],\ [73, 73, w + 59],\ [97, 97, w + 28],\ [97, 97, w + 68],\ [109, 109, 2*w - 7],\ [109, 109, -2*w - 5],\ [113, 113, w + 45],\ [113, 113, w + 67],\ [121, 11, -11],\ [127, 127, w + 39],\ [127, 127, w + 87],\ [137, 137, w + 37],\ [137, 137, w + 99],\ [139, 139, 4*w - 23],\ [139, 139, 4*w + 19],\ [149, 149, 6*w + 31],\ [149, 149, 6*w - 37],\ [151, 151, w + 60],\ [151, 151, w + 90],\ [157, 157, w + 53],\ [157, 157, w + 103],\ [163, 163, w + 54],\ [163, 163, w + 108],\ [169, 13, -13],\ [179, 179, 2*w - 19],\ [179, 179, -2*w - 17],\ [181, 181, w + 33],\ [181, 181, w + 147],\ [193, 193, w + 48],\ [193, 193, w + 144],\ [199, 199, w + 77],\ [199, 199, w + 121],\ [239, 239, w + 31],\ [239, 239, w + 207],\ [241, 241, w + 38],\ [241, 241, w + 202],\ [263, 263, w + 56],\ [263, 263, w + 206],\ [281, 281, 6*w - 35],\ [281, 281, 6*w + 29],\ [293, 293, w + 130],\ [293, 293, w + 162],\ [307, 307, w + 25],\ [307, 307, w + 281],\ [317, 317, w + 123],\ [317, 317, w + 193],\ [337, 337, w + 151],\ [337, 337, w + 185],\ [349, 349, w + 102],\ [349, 349, w + 246],\ [361, 19, -19],\ [367, 367, w + 81],\ [367, 367, w + 285],\ [401, 401, w + 40],\ [401, 401, w + 360],\ [419, 419, w + 50],\ [419, 419, w + 368],\ [431, 431, 2*w - 25],\ [431, 431, -2*w - 23],\ [433, 433, w + 197],\ [433, 433, w + 235],\ [439, 439, w + 187],\ [439, 439, w + 251],\ [443, 443, w + 89],\ [443, 443, w + 353],\ [467, 467, w + 167],\ [467, 467, w + 299],\ [499, 499, 4*w - 11],\ [499, 499, -4*w - 7],\ [503, 503, w + 155],\ [503, 503, w + 347],\ [509, 509, -4*w - 31],\ [509, 509, 4*w - 35],\ [521, 521, -6*w - 25],\ [521, 521, 6*w - 31],\ [529, 23, -23],\ [563, 563, w + 164],\ [563, 563, w + 398],\ [571, 571, -4*w - 1],\ [571, 571, 4*w - 5],\ [577, 577, w + 34],\ [577, 577, w + 542],\ [607, 607, w + 139],\ [607, 607, w + 467],\ [617, 617, w + 192],\ [617, 617, w + 424],\ [631, 631, 6*w + 41],\ [631, 631, -6*w + 47],\ [653, 653, w + 242],\ [653, 653, w + 410],\ [661, 661, w + 238],\ [661, 661, w + 422],\ [677, 677, w + 82],\ [677, 677, w + 594],\ [691, 691, w + 315],\ [691, 691, w + 375],\ [701, 701, w + 154],\ [701, 701, w + 546],\ [709, 709, 10*w - 59],\ [709, 709, 10*w + 49],\ [719, 719, w + 131],\ [719, 719, w + 587],\ [727, 727, w + 76],\ [727, 727, w + 650],\ [733, 733, w + 273],\ [733, 733, w + 459],\ [743, 743, w + 172],\ [743, 743, w + 570],\ [757, 757, w + 95],\ [757, 757, w + 661],\ [761, 761, w + 55],\ [761, 761, w + 705],\ [773, 773, w + 96],\ [773, 773, w + 676],\ [797, 797, w + 343],\ [797, 797, w + 453],\ [811, 811, 6*w - 49],\ [811, 811, -6*w - 43],\ [821, 821, -6*w - 19],\ [821, 821, 6*w - 25],\ [823, 823, w + 243],\ [823, 823, w + 579],\ [827, 827, w + 290],\ [827, 827, w + 536],\ [853, 853, w + 400],\ [853, 853, w + 452],\ [887, 887, w + 126],\ [887, 887, w + 760],\ [907, 907, w + 104],\ [907, 907, w + 802],\ [919, 919, w + 74],\ [919, 919, w + 844],\ [929, 929, 8*w + 53],\ [929, 929, 8*w - 61],\ [941, 941, 4*w - 41],\ [941, 941, -4*w - 37],\ [947, 947, w + 97],\ [947, 947, w + 849],\ [961, 31, -31],\ [967, 967, w + 256],\ [967, 967, w + 710],\ [983, 983, w + 297],\ [983, 983, w + 685],\ [991, 991, w + 308],\ [991, 991, w + 682],\ [997, 997, w + 470],\ [997, 997, w + 526]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, 1, 1, 4, -6, -6, -4, -1, -1, -1, -1, 8, 8, -2, 8, 8, 2, 2, 15, 15, 11, 11, -1, -1, -8, -8, 21, 7, 7, -16, -16, 11, 11, 14, 14, -17, -17, 14, 14, -13, -13, 22, 6, 6, -7, -7, 6, 6, -19, -19, -26, -26, 11, 11, 26, 26, -24, -24, 2, 2, 15, 15, -12, -12, -10, -10, -11, -11, 22, 27, 27, -12, -12, 30, 30, -6, -6, 7, 7, 0, 0, 4, 4, -18, -18, -12, -12, -8, -8, -28, -28, -8, -8, -35, -36, -36, -23, -23, -34, -34, 40, 40, 36, 36, 32, 32, -24, -24, -5, -5, -18, -18, 20, 20, 6, 6, 19, 19, 0, 0, 0, 0, 2, 2, 6, 6, -33, -33, -34, -34, 24, 24, -16, -16, 1, 1, 44, 44, 8, 8, -42, -42, -21, -21, -30, -30, 41, 41, 24, 24, 46, 46, -24, -24, -6, -6, 58, -31, -31, -54, -54, -47, -47, -55, -55] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w])] = -1 AL_eigenvalues[ZF.ideal([3, 3, w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]