# Stored data for newform 46.4.a.d, downloaded from the LMFDB on 23 April 2024. {"label": "46.4.a.d", "space_label": "46.4.a", "level": 46, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220398, "dim": 2, "is_polredabs": true, "nf_label": "2.2.73.1", "trace_hash": 334741827645951482, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-16, -3, 1]]], "qexp_display": "q+2q^{2}+(2-\\beta )q^{3}+4q^{4}+(4+2\\beta )q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 736, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 2.714087860264068, "hecke_ring_index": 1, "level_radical": 46, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [46, 1, [5], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 23], "conrey_indexes": [1], "field_disc": 73, "field_disc_factorization": [[73, 1]], "field_poly": [-18, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "1.950", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.574", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.765", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [23, -1]], "trace_display": [4, 3, 10, 12], "traces": [0, 2, 4, 3, 8, 10, 6, 12, 16, -13, 20, -12, 12, -51, 24, -58, 32, -66, -26, -16, 40, -128, -24, 46, 24, -54, -102, 9, 48, -57, -116, -17, 64, -18, -132, 352, -52, 206, -32, 325, 80, 373, -256, 314, -48, -284, 92, 859, 48, -30, -108, 120, -204, 50, 18, -60, 96, -754, -114, 612, -232, -1062, -34, -516, 128, -1058, -36, -844, -264, 69, 704, 399, -104, -1277, 412, -811, -64, -72, 650, 122, 160, -694, 746, 1802, -512, -768, 628, 1119, -96, 2046, -568, -1912, 184, 2493, 1718, 1380, 96, -910, -60, 78, -216, 1608, 240, -92, -408, -640, 100, -1108, 36, 604, -120, -1078, 192, -302, -1508, 230, -228, 1536, 1224, -1272, -464, -2590, -2124, -499, -68, -60, -1032, -3595, 256, 3464, -2116, -29, -72, 2824, -1688, 2162, -528, -3438, 138, 4445, 1408, 2201, 798, 306, -208, -2694, -2554, -1797, 824, 2406, -1622, -1057, -128, 1086, -144, -5122, 1300, 456, 244, 1462, 320, 276, -1388, 1949, 1492, 348, 3604, -3400, -1024, 1323, -1536, -2086, 1256, -3144, 2238, 2596, -192, -1272, 4092, 3209, -1136, 7474, -3824, -3710, 368, 3804, 4986, 396, 3436, 4288, 2760, -5178, 192, -3341, -1820, 2282, -120, -3753, 156, 2602, -432, -3310, 3216, -5160, 480, 3982, -184, -299, -816, 96, -1280, -4400, 200, 1365, -2216, -4416, 72, -10176, 1208, -2025, -240, 4092, -2156, 2648, 384, -1839, -604, 182, -3016, -3520, 460, 768, -456, 277, 3072, 2470, 2448, -766, -2544, -961, -928, 3200, -5180, -5664, -4248, 3354, -998, -7622, -136, 1900, -120, 8634, -2064, -276, -7190, 2352, 512, -5787, 6928, 6784, -4232, 3984, -58, 1306, -144, -2524, 5648, 2412, -3376, 10995, 4324, 7224, -1056, 3264, -6876, 324, 276, 6595, 8890, 7666, 2816, -6158, 4402, 4016, 1596, -996, 612, 6472, -416, -6334, -5388, 8636, -5108, 624, -3594, 7440, 1648, -54, 4812, -1173, -3244, -10088, -2114, -6786, -256, -1076, 2172, 5328, -288, -4956, -10244, 3031, 2600, -8538, 912, -5792, 488, -3668, 2924, 342, 640, 1258, 552, -3852, -2776, -6653, 3898, -12672, 2984, 1504, 696, -1023, 7208, -5500, -6800, -132, -2048, -5786, 2646, -1840, -3072, 102, -4172, 2712, 2512, -1334, -6288, -5516, 4476, -2765, 5192, -11873, -384, -3701, -2544, 462, 8184, 4224, 6418, 7326, -2272, 1010, 14948, -3885, -7648, -6166, -7420, 14952, 736, -5600, 7608, -5248, 9972, -16710, 792, 7356, 6872, 14703, 8576, 710, 5520, 119, -10356, 4060, 384, -2112, -6682, 6938, -3640, 17964, 4564, -1518, -240, -20155, -7506, 2508, 312, 1061, 5204, 1024, -864, 1684, -6620, 28137, 6432, 5290, -10320, -1236, 960, -10313, 7964, -15012, -368, 12432, -598, 10616, -1632, 1667, 192, -5642, -2560, 16752, -8800, -2846, 400, -2598, 2730, 2096, -4432, -1950, -8832, 7860, 144, 14004, -20352, 4062, 2416, -368, -4050, -14975, -480, -5061, 8184, -15765, -4312, 11544, 5296, 20034, 768, 26108, -3678, -2238, -1208, -235, 364, -21824, -6032, -1574, -7040, -6648, 920, -1341, 1536, -15968, -912, 5530, 554, 13224, 6144, 3112, 4940, -18296, 4896, -1884, -1532, 15032, -5088, 3836, -1922, -2628, -1856, -20510, 6400, -2944, -10360, -24552, -11328, 20389, -8496, 9311, 6708, -13439, -1996, 9108, -15244, 1704, -272, -672, 3800, -13125, -240, -6560, 17268, -33678, -4128, 26436, -552, -18492, -14380, -14413, 4704, -7224, 1024, 21098, -11574, 9176, 13856, -5154, 13568, 2730, -8464, 9370, 7968, -17582, -116, 3456, 2612, 15672, -288, 1058, -5048, -10548, 11296, -21155, 4824, -11380, -6752, 23611, 21990, 180, 8648, 6535, 14448, 10554, -2112, 30176, 6528, 12153, -13752, 552, 648, -23634, 552, 4528, 13190, -8748, 17780, 1824, 15332, 24916, 5632, -720, -12316, -14842, 8804, 1264, 8032, 13356, 3192, 7876, -1992, 10398, 1224, -2730, 12944, -1242, -832, 3415, -12668, 16779, -10776, 14024, 17272, -300, -10216, 18484, 1248, 14599, -7188, -50234, 14880, -13185, 3296, -13092, -108, -18624, 9624, 21642, -2346, -34856, -6488, -4629, -20176, -646, -4228, -12950, -13572, 6292, -512, 3648, -2152, -11867, 4344, -25148, 10656, -12934, -576, -5828, -9912, -5782, -20488, 207, 6062, 14904, 5200, -8442, -17076, 4524, 1824, -15120, -11584, -3084, 976, 3036, -7336, -28998, 5848, -18507, 684, -294, 1280, 17098, 2516, 3244, 1104, -3120, -7704, 8915, -5552, -3672, -13306, 1088, 7796, -12499, -25344, 40078, 5968, 7972, 3008, 21954, 1392, -18038, -2046, -12696, 14416, 20544, -11000, -1311, -13600, 5432, -264, 6372, -4096, 23785, -11572, 20927, 5292, -13686, -3680, -45464, -6144, 22684, 204, -723, -8344, 2520, 5424, 31220, 5024, 13982, -2668, 18640, -12576, 3096, -11032, 32226, 8952, -18660, -5530, -15535, 10384, 10412, -23746, 26092, -768, -23086, -7402, 46440, -5088, 25092, 924, -3640, 16368, -391, 8448, 6348, 12836, -11771, 14652, 22632, -4544, 18720, 2020, 18086, 29896, -22551, -7770, 13766, -15296, 19586, -12332, 7596, -14840, -5368, 29904, -2634, 1472, 5064, -11200, 14793, 15216, 3970, -10496, -39884, 19944, -20820, -33420, -14122, 1584, -18328, 14712, 17328, 13744, 30252, 29406, -7986, 17152, -53250, 1420, -414, 11040, 35991, 238, 57936, -20712, 15504, 8120, -39696, 768, -70968, -4224, -34851, -13364, -17016, 13876, -49911, -7280, -13184, 35928, 18186, 9128, -2394, -3036, -35187, -480, 40240, -40310, 24262, -15012, -64690, 5016, 3736, 624, 3794, 2122, 1324, 10408, -64038, 2048, -22872, -1728, -15270, 3368, 7662, -13240, 8096, 56274, 33027, 12864, -5396, 10580, -43161, -20640, 7624, -2472, -3030, 1920, -62372, -20626, 30824, 15928, 61176, -30024, 44495, -736, 4866, 24864, -61386, -1196, 23276, 21232, 28179, -3264, -9522, 3334, -14080, 384, -73113, -11284, 24660, -5120, -7405, 33504, 19160, -17600, 47568, -5692, -15540, 800, -20110, -5196, 4738, 5460, 29348, 4192, -18168, -8864, 25373, -3900, -61205, -17664, -23872, 15720, 26909, 288, -30612, 28008, -23955, -40704, -732, 8124, -962, 4832, 35918, -736, -30144, -8100, -9024, -29950, 46488, -960, -38270, -10122, 58832, 16368, -22128, -31530, 13931, -8624, -43616, 23088, 4164, 10592, -25122, 40068, -21550, 1536, 7475, 52216, 83595, -7356, 6672, -4476, -20096, -2416, 38684, -470, 5016, 728, -38046, -43648, 80170, -12064, -10812, -3148, 26564, -14080, 80272, -13296, -40440, 1840, 35440, -2682, -1743, 3072, 22178, -31936, -13856, -1824, 16677, 11060, 35280, 1108, 66341, 26448, 4608, 12288, -37712, 6224, -19304, 9880, 7620, -36592, 8579, 9792, 35456, -3768, 50051, -3064, 31359, 30064, -51346, -10176, 1548, 7672, -35964, -3844, -6714, -5256, 18792, -3712, 114339, -41020, 15962, 12800, -60286, -5888, 3729, -20720, 16560, -49104, 21344, -22656, 46672, 40778, -2205, -16992, -46524, 18622, -12276, 13416, -44660, -26878, 27502, -3992, -3654, 18216, -54976, -30488, 7222, 3408, 16648, -544, -3761, -1344, -22468, 7600, -11904, -26250, 41150, -480], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "46.4.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [2, 0], [2, -1], [4, 0], [4, 2], [4, -2], [4, 4], [8, 0], [-5, -3], [8, 4], [-6, 0], [8, -4], [-20, -11], [8, 8], [-28, -2], [16, 0], [-30, -6], [-10, -6], [-18, 20], [16, 8], [-64, 0], [-12, 0], [23, 0], [16, -8], [-37, 20], [-40, -22], [-10, 29], [16, 16], [-12, -33], [-56, -4], [26, -69], [32, 0], [-12, 6], [-60, -12], [160, 32], [-20, -12], [84, 38], [-36, 40], [158, 9], [32, 16], [172, 29], [-128, 0], [198, -82], [-24, 0], [-128, -28], [46, 0], [442, -25], [32, -16], [-39, 48], [-74, 40], [48, 24], [-80, -44], [44, -38], [-20, 58], [-24, -12], [32, 32], [-396, 38], [-24, -66], [276, 60], [-112, -8], [-560, 58], [52, -138], [-236, -44], [64, 0], [-476, -106], [-24, 12], [-450, 56], [-120, -24], [46, -23], [320, 64], [210, -21], [-40, -24], [-640, 3], [168, 76], [-434, 57], [-72, 80], [-24, -24], [316, 18], [48, 26], [64, 32], [-407, 120], [344, 58], [890, 22], [-256, 0], [-336, -96], [396, -164], [570, -21], [-48, 0], [1014, 18], [-256, -56], [-872, -168], [92, 0], [1294, -95], [884, -50], [648, 84], [64, -32], [-318, -274], [-78, 96], [30, 18], [-148, 80]]}