# Stored data for newform 74.3.g.a, downloaded from the LMFDB on 12 March 2025.
{"Nk2": 666, "analytic_conductor": 2.016353956266197, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 37, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 12, "char_parity": -1, "char_values": [74, 12, [39], [5]], "cm_discs": [], "conrey_index": 23, "dim": 8, "field_disc": 303595776, "field_disc_factorization": [[2, 8], [3, 4], [11, 4]], "field_poly": [81, 0, 45, 0, 16, 0, 5, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [4096, 0, -1088, 0, 225, 0, -17, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 412367192138, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 37, 7, -1, 12, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "74.3.g.a", "level": 74, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [2, 37], "level_radical": 74, "minimal_twist": "74.3.g.a", "nf_label": "8.0.303595776.1", "prim_orbit_index": 7, "qexp_display": "q+(-\\beta _{4}+\\beta _{5})q^{2}+(2\\beta _{1}-\\beta _{5}-\\beta _{7})q^{3}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c12", "self_twist_discs": [], "self_twist_type": 0, "space_label": "74.3.g", "trace_display": [4, 0, 12, 8], "trace_hash": 1551726509386058757, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "191.374", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6890.192", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.077", "prec": 17}, "traces": [0, 8, 4, 0, 0, 12, -4, 8, 16, -2, 24, 0, -4, -10, 16, -72, 16, -26, 2, -70, 24, -30, -20, 24, 4, 36, 20, 0, -12, -38, -138, 72, -16, -4, -8, -28, 0, 12, -76, -28, 24, 138, -34, 80, 16, -6, 24, 48, 0, 166, 48, 202, -20, -102, -14, -32, 4, 266, 126, -206, -12, 74, -12, -8, 0, 36, -8, -408, -16, 210, 62, 28, -4, 0, 6, -276, -140, 36, -18, 46, 48, 272, -108, -36, -16, 0, 80, -154, 32, -418, -6, -44, -180, -378, -36, -408, -8, 142, -142, -60, 48, 0, 162, -112, -60, 2, 186, 404, 28, -540, 0, -204, 64, -14, 414, 66, 88, 28, 214, 30, -12, 824, 0, 324, 60, 300, 32, 416, 32, -838, 58, 150, 144, -50, 308, 594, -120, -104, 0, 396, 124, -168, 56, 92, 8, 28, -472, 0, -108, -284, -552, 396, -204, -148, 0, 674, -76, -168, 124, 0, 48, -78, 544, -598, -108, -148, -654, 226, -68, -42, -368, -80, 52, -288, -424, 0, -48, 58, -660, 648, 132, 358, 46, -788, 0, -504, 192, -216, -120, 318, -758, -208, 16, -878, 142, 176, 0, 860, -64, -128, 96, 154, -102, -334, 364, -370, 444, 120, 40, 80, -366, 208, 0, 582, 808, -210, 56, 350, 300, 124, 64, 0, 564, -440, 8, 378, -18, -62, 236, 752, -348, 0, -152, 0, 28, -972, 428, -1178, 30, -210, -264, -50, 460, 0, -148, 346, -558, -216, 288, 0, 372, 20, 72, 336, -146, 758, -64, -366, 0, 92, 88, 110, 102, 888, 136, -1894, -146, -110, 308, 1208, 0, 932, -136, 10, 158, 276, -420, -648, 318, 348, 12, 788, 1032, 322, 444, 2132, 0, 60, 16, -912, 56, 298, 32, -874, -236, 0, -276, -56, -622, -318, -828, 218, 724, 144, -152, -1326, -388, 0, 0, -842, 1348, -1378, -76, -2120, -864, 148, 92, -1368, -1062, 224, 0, 522, 120, 0, 0, 204, -534, -150, 384, 144, 236, -914, 0, -384, 1180, -1168, -120, -126, -646, -1810, -260, 416, -80, 1336, 0, 846, -504, -528, -308, 1034, 48, 70, -16, 586, 726, 1344, -352, 162, -564, 1344, 0, 2058, 716, -288, 92, -72, -350, -760, 360, 0, 562, -1328, -756, 192, -300, -102, 96, -84, -56, 168, -1400, 0, -208, -290, 32, 116, -878, -812, -664, 202, -194, 306, 284, 330, -1592, 3240, -16, 0, 348, 370, 144, 1412, 578, 182, 612, 660, 0, -68, 808, 1794, -936, 852, 332, -318, -120, -490, 40, 1596, 0, -248, -364, 874, 1388, -540, -372, 816, 238, -424, -108, 244, 2220, -1134, 0, 2712, 0, -66, 600, 6, 248, 974, -152, 50, -154, 0, 948, -1364, -1276, -2136, -48, -82, 252, -356, -20, -874, -1556, 0, 236, -1446, 1504, -1366, -348, 566, -84, 554, 176, -2190, -354, -1800, 20, -1278, 552, 0, -396, -896, -774, -2268, 276, 48, -186, -206, 0, -282, 1084, 270, 96, 24, -592, -2144, 80, -1154, 346, 336, 0, 992, -246, -160, 120, 286, -558, 1122, 672, -1730, 2088, -146, -16, 1050, -648, 604, 0, -2256, 1516, 1068, -128, -1076, -720, 538, 1676, 0, 416, -1632, 116, -834, -30, 970, 396, -234, -52, 218, -32, 0, -1894, -400, -292, -52, -110, -384, -1124, -186, -524, -516, -1188, 50, -2006, 2964, -64, 0, -78, -1208, 420, 310, -48, -762, 288, 578, 0, 1316, -312, 826, 864, 426, 136, 132, -376, 804, 1032, -444, 0, -544, 500, -942, 2590, 1088, -184, 1418, -62, -60, 0, 3466, 632, 2494, 1188, 700, 0, 672, 64, 246, -1748, -146, 232, -1666, -110, 0, -360, 3908, -580, 1494, -960, 1166, 516, -580, -552, -624, 1112, 0, 724, 1244, 288, 226, -152, 526, 768, -456, -296, -1158, -412, -890, 72, -786, -1472, 0, -348, -1104, -978, -66, 40, -544, 340, 304, 0, -1938, -128, 838, 60, 1008, -1124, 1122, -300, 344, 224, 632, 0, -1812, 650, -2728, -156, -1578, 842, 2870, 544, -168, 528, -1442, -1324, -1450, -1062, -2692, 0, -960, 288, 3576, 472, -276, -494, 226, 1308, 0, 474, -1008, 452, 1320, -1686, 1064, -32, 306, 1276, 1146, -2416, 0, -1810, -202, -520, 1186, 416, 3890, -232, -2090, 206, 408, -104, -982, -1176, -2760, -864, 0, -348, -278, -192, 980, -1556, -1368, 276, 1814, 0, 774, 128, 1608, 1584, 348, 784, 88, -618, 1520, -352, -1656, 0, 168, 84, -3438, 1392, 60, -264, -1026, 2042, 1312, 1476, 810, -148, 2734, -84, -4832, 0, -4362, -700, 2130, -1520, -2564, -96, 1068, -366, 0, -644, -36, -442, -696, -1704, -1452, 904, -480, -264, -670, -2676, 0, 96, 2542, -168, 3220, -56, 128, 378, 12, -1516, -2712, -898, -1474, 1324, -378, -1052, 0, 0, -748, 108, -1026, 188, -800, 304, -312, 0, -898, 3616, 1232, -564, 300, 408, 2212, -664, 1456, 330, -1904, 0, -614, 3854, -110, -128, -680, 2890, 3038, 220, 578, 1014, -1236, 96, -44, -2556, -2560, 0, -366, 364, 4392, 1224, -1838, 816, 192, 668, 0, 780, -2300, 728, -2274, 3636, 32, 392, -1350, 1768, 1920, -448, 0, -318, 3254, -240, 486, -490, 2316, -160, -1176, 930, 5364, -160, -1440, -430, 228, 8, 0, -918, -3574, 2568, -2074, 768, 888, 408, 2966, 0, -528, -1376, 4008, -54, -1116, 700, 4846, -212, -1800, 2220, 716, 0, -4984, 56, -3488, 2862, 898, -700, 1408, -1136, -968, -1560, -34, 1428, -754, 2832, -204, 0, 4368, -304, -1092, 100, -3102, -112, 1748, -2168, 0, -636, 1196, -1540, 1476, -2112, 3156, 1792, 294, 128, -426, -508, 0, 252, 5666, -712, -1594, -20, 4742, 742, -4922, -124, 888, -174, -4384, 592, -2196, -4248, 0, 480, -502, -978, -228, 480, -1172, -2014, 184, 0, -1878, -1036, 676, 504, -3474, -2692, -1396, -468, 4090, -1800, -1312, 0, 102, -942, 1150, -1944, -150, 2538, 4506, 32, 1366, 552, -2370, -3164, 1616, -3288, -8824, 0, -3294, 96, 2946, -372, 164, -962, -528, 528, 0, -548, -1064, -100, -834, 504, -2626, 1648, -2924, -52, 388, -2368, 0, -2144, -150, 160, 398, -1154, -792, 356, 846, -900, -2136, 1116, 880, -590, -1044, -120, 0, 72, -800, -48, 1270, -1018, -414, 888, -662, 0, 1416, 1200], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1, 0, 0], [0, 2, 0, 0, 0, -1, 0, -1], [0, 0, 0, -2, 0, 0, 0, 0], [1, 0, 2, 0, 0, 1, -2, 2], [0, 1, -2, 1, 1, 0, 1, 1], [2, 0, 0, 0, 2, -1, 0, 1], [2, 0, 0, -2, 0, -2, 0, 0], [-1, 0, 1, 0, 0, 0, -2, 0], [3, -4, 0, 1, 0, 3, 0, 4], [-2, 0, 0, 2, -2, 2, -2, 0], [2, 0, -2, 0, 2, 0, 4, 0], [0, -1, 1, -2, 2, -2, 0, 1], [2, -1, 0, 3, -1, 2, 1, 1], [-10, 4, -4, 10, -3, 3, 3, -3], [0, 0, 0, 0, -4, 0, 0, 0], [-8, 1, 1, -8, -4, -4, -6, -6], [0, -2, -1, 1, 1, 1, -1, 1], [-7, 3, -7, -3, 3, -10, 4, -7], [2, -4, 4, -2, -4, 4, 0, 0], [-5, 2, 1, -2, -3, -2, 0, -4], [-2, -2, -2, -2, 2, 2, 0, 0], [10, 1, 4, 1, 11, -10, 1, -5], [2, 4, 2, 0, 0, -2, 2, -2], [6, -4, 12, 4, -3, 5, 0, 8], [2, -1, 2, 3, -1, -2, -1, 1], [0, -9, 0, -1, 0, 8, 0, -9], [-2, 0, 2, 0, -2, 4, 0, 0], [-1, 3, 7, -8, 7, -1, -3, 4], [-9, 6, -5, 0, 14, -3, 5, -3], [16, -15, -4, 15, 1, 16, 15, 11], [-4, 0, 0, -4, -4, 0, 0, 0], [-2, 0, -2, 8, 0, 12, -2, 4], [-5, 0, -6, -7, 1, -10, -6, -4], [0, 6, 6, 0, 5, 5, -1, -1], [0, -2, 0, 0, 0, 2, 0, -2], [-4, -4, -18, -17, -7, -15, 5, 7], [-8, 11, -6, 3, 3, -14, 3, -11], [0, -2, 2, 0, 3, -3, 3, -3], [-2, 0, 8, -6, -6, 0, -8, 0], [9, 18, 5, 9, -14, -9, -5, -9], [-5, 4, -1, -2, 2, -7, -3, -1], [-4, -17, -8, -3, -7, 4, -17, 25], [4, 0, 0, -4, 4, -4, 0, -4], [-7, -2, 3, -5, -12, 7, -2, -1], [-4, 6, 4, 26, -8, 10, -8, 0], [14, -6, -32, 8, 16, -2, 16, 6], [0, 4, 0, 4, 0, 0, 0, 4], [-1, 4, 1, -4, -42, -4, -2, 0], [2, -8, 16, 8, -8, 10, -8, 16], [35, -6, 5, 24, 11, 35, 6, 11], [-6, -2, 2, 6, -6, 6, -2, 2], [3, 38, -3, -14, 27, -26, 6, 0], [-9, 9, 9, -9, -1, -1, -18, -18], [-10, -6, -4, -8, -8, 2, -2, 4], [2, 0, 2, -4, 4, -2, -2, 2], [29, -21, 21, -29, -8, 8, -11, 11], [21, -7, 1, 7, 10, -6, 0, 14], [-19, -7, -7, -19, 22, 22, -5, -5], [14, 8, -6, 12, 26, -14, 8, -2], [27, 10, -25, 13, 13, -14, 35, 25], [-2, 4, 26, -4, -14, 16, 0, -8], [-2, 2, 4, -4, -2, 2, -2, -2], [0, 0, 0, -8, 0, -8, 0, 0], [6, 3, 8, -3, -1, 4, 0, -6], [8, -6, -4, -6, 14, 8, 6, 2], [-26, 14, -16, -42, 42, -7, 16, -7], [-6, -2, -12, -2, -4, -6, 2, -10], [21, 8, 25, -6, -6, -27, -17, -25], [15, 0, -1, 6, 16, 1, -1, 11], [12, 0, 10, 8, 2, 37, 10, -21], [-2, 2, 2, -2, 0, 0, -4, -4], [-56, -4, 0, 2, -76, 6, -36, -4], [-2, -2, -9, -27, -22, -26, 21, -15], [-32, 15, -10, 27, 5, -42, 5, -15], [-14, 14, -14, 14, 8, -8, 6, -6], [2, 0, 2, 0, -4, 0, -2, 0], [-5, 6, 7, 8, -2, -3, -7, -3], [15, -47, 35, 11, -11, 26, 12, 35], [0, -8, 0, -4, -4, 0, -8, 8], [73, 0, 10, 0, 63, 0, 10, 0], [-23, 4, -18, 9, -14, 23, 4, 14], [-14, -7, 14, 115, 2, 61, -28, 0], [0, -2, -8, 6, 4, -4, 4, 2], [-51, -21, 0, -43, -83, -22, -19, -21], [8, -42, -8, -22, -16, 10, 16, 0], [-21, -6, -13, 16, -16, -5, 19, -13], [0, 4, 0, 4, -4, 0, -4, -4], [-58, -1, 1, 58, -6, 6, -6, 6], [-3, -1, 3, -21, 0, -10, -6, 0], [-4, 2, 2, -4, 3, 3, -1, -1], [-18, -8, -10, 12, 12, 30, 2, 10], [-25, 16, -13, -54, 54, -79, -3, -13], [6, 10, -10, -6, -6, 6, 32, -32], [-68, 27, -40, -27, -14, -101, 0, -54], [4, -4, -4, 4, 4, 4, 8, 8], [37, -5, 9, 2, 39, -37, -5, -4], [-38, -2, -5, -41, -41, -3, 3, 5], [-10, -2, -2, 2, -4, 0, 0, 4], [2, -24, 16, 6, -8, 18, -8, 24]]}