# Stored data for newform 78.3.l.c, downloaded from the LMFDB on 19 April 2024. {"label": "78.3.l.c", "space_label": "78.3.l", "level": 78, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007955219316814, "dim": 8, "is_polredabs": true, "trace_hash": 795812693295924188, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [5253264, -632592, 38088, 11916, 4065, -282, 18, 6, 1]]], "qexp_display": "q+(-\\beta _{4}-\\beta _{5})q^{2}+(2\\beta _{2}-\\beta _{5})q^{3}+(2\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 12, "char_parity": -1, "char_degree": 4, "char_conductor": 13, "char_orbit_label": "l", "char_is_real": false, "Nk2": 702, "analytic_conductor": 2.125346062010316, "hecke_ring_index": 1, "level_radical": 78, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.085", "prec": 17}, "analytic_rank_proved": true, "char_values": [78, 12, [53, 67], [12, 11]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 13], "conrey_indexes": [7, 19, 37, 67], "field_disc": 31282812354816, "field_disc_factorization": [[2, 8], [3, 6], [11, 4], [107, 2]], "field_poly": [5635876, 275384, 6728, -6736, 5053, 82, 2, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "7.739", "prec": 17}, {"__RealLiteral__": 0, "data": "1.485", "prec": 17}, {"__RealLiteral__": 0, "data": "203.068", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8907.569", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c12", "trace_display": [4, 0, -6, 10], "traces": [0, 8, 4, 0, 0, -6, 12, 10, 16, -12, -6, 24, 0, 0, 4, -12, 16, -84, -24, 10, -12, 18, -12, -12, -24, 0, 26, 0, 20, 36, -18, -94, -16, 0, 60, -204, 0, 140, 0, 66, -24, 72, 18, -222, -24, 0, -84, 300, 0, 42, -62, 0, 44, 84, -36, 396, 36, 24, -66, -60, -12, -90, 198, -24, 0, -108, 72, 304, 60, -216, -408, -192, -24, 16, -46, 312, -20, 0, 114, -96, -24, -36, 114, 0, -12, -390, 168, 30, 72, 354, 0, -218, -288, -42, 300, -576, 0, -460, 58, -36, 208, -18, -174, 0, 88, -96, -150, -144, -72, -578, -312, 48, 8, 48, 132, 732, 0, 144, 24, 420, -12, -24, -180, -12, 104, 654, -6, -120, 32, 0, 618, -312, 0, 202, 534, 18, -228, 942, -24, 22, -96, -408, 0, -792, -96, 1032, 16, 48, -92, -342, 354, -172, 88, 252, -372, 0, 192, 404, -486, -192, -24, 276, 36, -244, 60, -84, -408, 360, 0, 100, -468, 102, 168, -420, 60, -220, 48, -132, 228, -12, 0, 0, 330, -444, -168, -966, -282, 120, -216, -36, -384, -432, -96, 358, 0, 0, 64, 378, -36, 324, 416, -156, -150, -324, 168, -1824, -546, 0, 192, 984, -660, 72, -384, 228, 108, 756, 0, 158, 738, 138, 0, -204, 468, 1198, 8, 126, 96, 480, 156, -896, -216, 1260, 132, 0, 132, -360, -120, -438, 720, 1032, -24, -1504, -760, 0, -444, -780, 0, -334, -376, -204, 654, -384, -12, 1848, 262, -546, -64, 270, -474, 0, 444, -216, -636, -348, -72, -66, 320, 810, 148, 180, 54, -22, 0, -438, 804, -1632, -24, 1074, 44, 438, -504, 330, -84, -444, 384, 0, 276, -408, -48, 86, 1806, 918, 308, 432, 84, -240, 468, 108, 0, -612, 168, -672, -172, -396, 176, 1836, 162, 2, 840, 252, -660, 0, 228, 1920, 16, -612, -876, -306, 318, -2004, -48, 36, -1452, -684, 0, -1480, -532, -498, 60, -492, -168, 796, -408, -138, 48, 204, 24, 0, -1006, -444, -780, -504, 72, 270, -612, 300, 288, -324, -216, 178, 0, 0, -96, -2046, -132, 2364, 456, -180, 192, -384, 36, -1584, -750, 0, -356, 1860, -492, 422, -48, -90, 942, -912, 396, 1104, 1776, -600, 0, 1026, -108, 362, -384, 1146, -864, 1008, -96, 456, -320, 666, 920, 0, -600, -1704, 116, -480, 672, 1116, 144, -26, -788, -522, 168, -1326, 0, -836, -528, 54, -324, 888, 336, -1274, -1578, 1482, 168, -2316, -180, 0, 280, 768, 1584, 288, -1224, 580, 474, -576, 168, 1146, -468, 1878, 0, -156, 1224, 60, 0, 1170, 316, -516, 160, 24, -324, 1326, 624, 0, -738, 2088, 96, 174, 2376, 414, 64, 270, 624, -468, -444, 186, 0, 3108, 96, -1000, -896, -270, -432, 522, 1308, -718, -144, -36, -156, 0, 132, -20, 720, -186, -264, -2172, 294, 790, 240, -126, -1824, -1248, 0, 1106, -1372, -312, -760, -1722, 0, -1594, -624, -222, -342, 36, 24, 0, -676, -2376, 208, 132, 0, -412, 108, 456, -96, 180, -108, 834, 0, -1056, 1528, -1836, -546, -642, -128, 162, 786, -2580, 444, -1152, 616, 0, -660, -672, -18, 1232, -960, 1182, -648, 1344, 144, 644, 1974, 216, 0, 480, 1872, -276, 148, 612, 360, -1488, 72, 1000, -1078, -558, 456, 0, -312, -4436, 1884, -270, -2196, 2448, -408, 432, -528, 24, 768, -756, 0, 168, -1632, 1068, 330, -2532, -168, -1002, 314, -18, -312, 1056, 0, 0, 504, -1224, 1608, 1980, 0, -3442, -686, -282, 516, 1608, -6, -1020, 0, 846, -684, 672, 84, -114, -480, -210, 376, -1506, -108, 2604, 684, 0, 156, 1992, 708, 240, -426, -222, 28, 2970, -36, -868, 96, -348, 0, 3108, -360, 3302, 2, 738, 1680, 210, -210, -1250, -24, 648, 1656, 0, 264, 1924, 2682, 1092, -372, -3138, 468, 1588, -192, -546, 114, -336, 0, 206, -1584, 108, -48, -2304, 72, -2402, -1176, 900, -696, 2400, -72, 0, -2780, 864, -488, 1380, -1734, 672, 168, -510, 144, -300, -2376, -2290, 0, -204, 0, -132, -138, -492, 96, -1158, 444, 4092, -72, 1494, 2156, 0, -2112, 288, -78, -358, -1092, -432, 36, -1920, 264, -804, 1026, 2124, 0, 1848, 2496, -1762, 288, 144, -648, -5880, -156, 846, 142, 936, 440, 0, -54, -2272, 96, 900, -4002, -1644, 168, 1868, -648, 144, 1872, -1332, 0, 4092, 816, 636, -384, 492, 72, 1218, -1264, -2322, -372, -3570, 1116, 0, -956, 216, 1434, 1524, -540, 728, -1634, -1464, -576, -168, -342, 982, 0, -594, -336, 4116, 396, -1608, 2208, -612, 1896, 1788, -762, 2268, 432, 0, -876, -2640, -72, -84, 414, -2856, -768, 246, -240, 508, -1224, 468, 0, -204, 0, -1840, 456, 1548, -640, 5046, 414, 1058, -4, -2478, -906, 0, 912, -96, 504, 90, 168, -8526, 12, -1774, 168, 996, -2076, -684, 0, 354, 1252, 888, -788, -504, -1044, -3732, 584, 684, 1074, -1932, 312, 0, 220, -4008, -300, 2196, 54, 3118, -1344, -2178, 3120, -2748, -360, -582, 0, 1398, 984, -3426, 1482, 912, 336, -504, -2148, 2088, 432, 4818, 2976, 0, 352, 1764, 450, -2016, 2184, -594, 1128, -2244, -192, 94, 972, 330, 0, -2220, -1800, -3350, 168, 2274, 2292, -1296, -240, 3932, -2226, 1728, -216, 0, -2244, -1080, 1512, 1812, -840, 540, -144, 2712, 1508, 600, 864, 4656, 0, 1070, -2312, 1374, 24, 4764, -648, 1418, 378, 1206, -1584, -4218, -78, 0, -600, 4800, -1104, 1356, -276, -3058, 72, -108, 40, 2988, -810, -4284, 0, 1248, 1968, -780, 624, -3048, -936, -1164, -348, 3246, 144, 4560, -960, 0, 3420, 3384, 312, -3216, -1596, -1578, 2456, 780, 504, -1680, 2496, -114, 0, -2556, 192, 688, -718, -1386, -288, -2256, -708, 1852, 624, -2664, 756, 0, 156, -2940, -370, 1722, 1800, 1152, 792, -804, 48, 144, 36, 3648, 0, 1120, 184, -402, 240, -1740, -252, 4776, -792, -3216, 552, 120, 48, 0, -1560, 864, -3008, -1428, 828, 3748, 712, -2076, -204, -204, 216, -6220, 0, -1578, -720, -360, -222, 1632, -684, 1974, 2052, -2004, -228, 654, 1758, 0, -1328, -2448, -1440, 184, 792, -318, -2148, -6168, -816, -664, -3000, 558, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 6, -1, 12, 0]], "char_orbit_index": 12, "prim_orbit_index": 6, "minimal_twist": "78.3.l.c", "char_is_minimal": true, "conrey_index": 7, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": 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, 0, 2, 0, 0, -1, 0, 0], [0, 0, 2, 0, 0, -2, 0, 0], [0, 0, 1, -1, 0, 0, -1, 0], [1, 0, 1, 0, -1, 1, 0, 0], [1, -1, 0, 0, 0, -1, 0, -1], [2, 0, 2, 0, 0, 0, 0, 0], [-3, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 2, -1, 1], [2, 0, -2, 0, 0, 2, 0, -2], [-2, 0, 0, 0, -4, 0, 0, 0], [4, 0, -6, 1, 8, 1, 0, 1], [0, -1, 1, 1, 0, -2, 1, 0], [-2, 2, -2, 0, -1, 1, 0, 1], [0, 0, 0, 0, -4, 0, 0, 0], [-7, -1, 7, 0, 7, -7, 1, 0], [-3, 0, 3, 0, 0, 0, 0, 0], [6, -1, -7, -1, 7, 5, 0, 1], [-2, 2, -2, 0, -2, 2, 0, 2], [2, 0, 2, -1, -1, -1, 1, 0], [-4, -2, -2, 2, -2, -2, 0, -2], [-2, 2, 0, -2, -2, 16, 0, 0], [-4, 0, 4, 0, -2, -2, 0, 0], [1, 1, -26, 2, 6, 0, 1, -1], [7, 2, -9, 0, 8, -2, 1, 1], [0, 0, -3, 0, 0, 6, 0, 0], [2, 0, 2, 0, 0, -2, 2, 0], [-3, 3, -6, 3, -11, 3, 1, 1], [-1, 1, 0, -1, 2, 0, -2, -1], [-4, -1, 21, 0, 17, -17, 0, -2], [-4, 0, 4, 0, -4, -4, 0, 0], [0, 0, 4, 2, 4, -2, 4, 0], [15, -1, 0, -1, 14, 14, 1, 0], [-48, 0, 4, -2, -50, 4, -2, 2], [0, 0, 0, 0, 0, 6, 0, 0], [22, 0, -22, 0, 4, 18, 0, 5], [4, 0, -12, -2, 4, 0, 0, 2], [12, -1, 2, -1, 7, -13, -2, -2], [-2, 2, 0, -2, 0, 0, -2, 0], [12, -6, 12, 0, 5, -7, -2, -3], [2, -2, 2, -2, -3, -1, -1, -1], [-19, 2, 21, 1, 18, -21, -1, 1], [-4, 0, 4, 4, 4, -4, 4, 0], [0, 0, -3, 3, 3, 3, 0, 0], [-16, -2, -14, -2, -14, 18, -4, -2], [34, 0, 42, 2, -6, -6, -2, 0], [0, 0, 4, 0, 0, 4, 0, 0], [5, -3, 0, 3, 4, -2, 2, -2], [4, 0, -6, 2, 29, -23, 1, -3], [-5, -1, -21, -2, -14, 0, -1, 1], [12, 0, -6, -2, 12, -10, -2, -2], [11, 1, -17, 2, 0, 34, -1, 3], [-6, 0, -6, 0, -3, 3, 0, 0], [4, -4, 16, -4, -96, -8, -2, -2], [4, -2, 2, -2, -2, -2, 0, -2], [12, 1, 3, -3, 12, -12, -3, 2], [-15, 3, 8, 1, -8, -14, 0, -3], [2, -2, 12, -4, 12, 2, -8, -2], [0, 0, -2, 2, 4, 4, -2, 0], [-25, 7, 15, -3, -28, 15, 4, 3], [32, -2, 0, 2, 17, 25, 1, -1], [-3, 0, 3, 0, -3, 0, 0, 3], [0, 0, 8, 0, 0, 0, 0, 0], [8, -6, 54, -4, 39, -55, 4, -1], [8, -2, -2, -2, 0, 4, 2, -4], [45, 2, 45, 0, 13, -32, -2, 1], [2, -2, -28, -2, -14, 14, 0, 0], [-20, 2, -6, 4, 16, 6, 2, 4], [-52, 2, 46, -2, -8, 8, -2, 4], [-32, 4, 12, -2, -12, -34, 0, -4], [-6, 0, -6, 0, -6, 6, 0, 0], [-14, 5, 16, 1, -29, -29, -1, 0], [-9, 5, -22, -5, -14, -22, 0, 5], [49, -3, 0, 3, 26, -9, 3, -3], [8, 0, -4, -4, 14, -10, -2, 2], [4, -4, -100, 2, 12, 0, -4, -6], [17, -1, 6, 3, 7, -15, 0, 1], [-12, 0, -34, -5, 0, 68, 0, -5], [0, 0, 0, 0, 4, 4, -4, 0], [0, 0, 0, 0, 9, 0, 0, 0], [7, -1, 2, 5, -12, -2, 6, 5], [-26, 2, -24, 10, -40, 40, 10, 4], [-2, -2, 4, 0, -4, -2, 0, 2], [-61, 9, -17, 6, -17, 55, 12, 9], [38, 3, 3, 1, 36, 36, -1, 0], [4, -4, 11, 5, 9, 11, 1, -5], [8, 0, 0, 0, 4, 4, 4, -4], [80, 0, -78, -2, 68, 10, -1, 1], [-3, 3, -6, 3, 0, 0, 3, 0], [-5, 6, 29, 6, 56, 7, 1, -2], [-36, 0, -4, 4, 0, 8, 0, 4], [-25, 0, -25, 0, -38, -13, 3, 0], [-4, 4, 12, 4, -78, -6, 2, 2], [-46, -4, -46, -4, 50, 46, 0, -4], [-4, 0, -4, 0, -8, 8, 0, 0], [-34, -4, -40, -1, 40, -35, 0, 4], [3, -1, -2, 3, -2, -6, 6, -1], [-6, -6, 0, 0, -6, -6, 0, 0], [48, -2, -6, 4, 52, -6, 2, -4]]}