# Stored data for newform 425.4.b.c, downloaded from the LMFDB on 23 April 2024. {"label": "425.4.b.c", "space_label": "425.4.b", "level": 425, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007268041327017, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 688235009755179611, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [9, 0, 1]], [3, [64, 0, 1]]], "qexp_display": "q+3iq^{2}-8iq^{3}-q^{4}+24q^{6}+28iq^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 6800, "analytic_conductor": 25.075811752439762, "hecke_ring_index": 1, "level_radical": 85, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [425, 2, [52, 326], [1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [5, 17], "conrey_indexes": [324], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.887", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.451", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "162.425", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, -2, 0, 48, 0, 0, -74, 0, -48, 0, 0, -168, 0, -142, 0, 0, -232, 0, 448, 0, 0, 336, 0, 348, 0, 0, -60, 0, -344, 0, 0, 102, 0, 74, 0, 0, -928, 0, -684, 0, 0, 48, 0, 360, 0, 0, -882, 0, -272, 0, 0, -480, 0, -1176, 0, 0, -504, 0, 220, 0, 0, -866, 0, -1152, 0, 0, -960, 0, -1416, 0, 0, -348, 0, 232, 0, 0, 968, 0, -718, 0, 0, -448, 0, 888, 0, 0, 1548, 0, 3248, 0, 0, 1728, 0, -720, 0, 0, 1776, 0, -420, 0, 0, 2436, 0, -1908, 0, 0, 2372, 0, 928, 0, 0, -5568, 0, 60, 0, 0, 952, 0, -1510, 0, 0, 344, 0, 6216, 0, 0, -2368, 0, 5520, 0, 0, -2904, 0, 714, 0, 0, -5056, 0, -4608, 0, 0, 5254, 0, -2172, 0, 0, -3228, 0, -6656, 0, 0, 4032, 0, 928, 0, 0, 5088, 0, 3360, 0, 0, 684, 0, -4536, 0, 0, -2334, 0, 8584, 0, 0, -1440, 0, 3408, 0, 0, 7032, 0, 6796, 0, 0, 2520, 0, -8256, 0, 0, -4480, 0, -5280, 0, 0, -2292, 0, 882, 0, 0, 6440, 0, 7744, 0, 0, 272, 0, 1392, 0, 0, 5568, 0, -4160, 0, 0, 2592, 0, -3360, 0, 0, 5792, 0, -1972, 0, 0, 2520, 0, 2196, 0, 0, 2372, 0, -10752, 0, 0, -12876, 0, 504, 0, 0, -10656, 0, 11236, 0, 0, -220, 0, -16416, 0, 0, 12096, 0, -4056, 0, 0, -2832, 0, 3026, 0, 0, -3248, 0, 2220, 0, 0, -8064, 0, 19488, 0, 0, 7140, 0, 544, 0, 0, 6588, 0, 960, 0, 0, 12728, 0, 17748, 0, 0, 1416, 0, -8352, 0, 0, -578, 0, 6112, 0, 0, -21168, 0, -2436, 0, 0, -6960, 0, 8288, 0, 0, 16472, 0, -3774, 0, 0, -3712, 0, -7944, 0, 0, -14748, 0, -968, 0, 0, 1440, 0, -6912, 0, 0, 718, 0, -1632, 0, 0, 16128, 0, -9128, 0, 0, 21096, 0, -31808, 0, 0, -5856, 0, 8256, 0, 0, 6216, 0, 11052, 0, 0, -22252, 0, 9280, 0, 0, -12096, 0, -1548, 0, 0, -10080, 0, 13194, 0, 0, -3248, 0, 5280, 0, 0, 25308, 0, -17808, 0, 0, -2448, 0, 12096, 0, 0, -640, 0, 7552, 0, 0, -26544, 0, -17292, 0, 0, -2748, 0, -2040, 0, 0, -252, 0, -1776, 0, 0, -51968, 0, 5412, 0, 0, 420, 0, 5040, 0, 0, -532, 0, -17568, 0, 0, -13320, 0, -5220, 0, 0, -5376, 0, -27620, 0, 0, -13356, 0, -33984, 0, 0, 22272, 0, 6072, 0, 0, 28896, 0, -2372, 0, 0, 104, 0, 32634, 0, 0, -928, 0, -27984, 0, 0, -12228, 0, 16416, 0, 0, -8640, 0, -38976, 0, 0, 2720, 0, 6732, 0, 0, 4260, 0, 32004, 0, 0, -27104, 0, 39328, 0, 0, 23232, 0, -952, 0, 0, -10344, 0, 6728, 0, 0, 1510, 0, -30192, 0, 0, 4352, 0, 17400, 0, 0, -40368, 0, 24424, 0, 0, 2336, 0, -56256, 0, 0, 43512, 0, -8640, 0, 0, 25140, 0, -20272, 0, 0, -11412, 0, 2368, 0, 0, -29472, 0, 23316, 0, 0, -5520, 0, 32832, 0, 0, 17134, 0, 18648, 0, 0, 37152, 0, -20328, 0, 0, 21168, 0, 35644, 0, 0, -1530, 0, 77952, 0, 0, -8140, 0, 6960, 0, 0, 22980, 0, 5056, 0, 0, -17168, 0, 6528, 0, 0, 4608, 0, 15792, 0, 0, -43668, 0, -42416, 0, 0, 57456, 0, 32042, 0, 0, 46112, 0, -42336, 0, 0, -15204, 0, 38412, 0, 0, 39904, 0, 672, 0, 0, 11520, 0, 3228, 0, 0, -11568, 0, -8396, 0, 0, 6656, 0, -10080, 0, 0, -13440, 0, -33408, 0, 0, -53880, 0, 28224, 0, 0, 34448, 0, 9600, 0, 0, 65888, 0, -28380, 0, 0, 1972, 0, -24896, 0, 0, -17388, 0, -5088, 0, 0, 52392, 0, -50364, 0, 0, -3360, 0, -11832, 0, 0, 12096, 0, -77056, 0, 0, 56928, 0, 48564, 0, 0, -56184, 0, 21820, 0, 0, -31752, 0, 12876, 0, 0, 74624, 0, -5280, 0, 0, 4332, 0, 2334, 0, 0, -21392, 0, 23040, 0, 0, -8584, 0, 16464, 0, 0, 36888, 0, 36640, 0, 0, 33264, 0, -10080, 0, 0, -85344, 0, -45780, 0, 0, 20784, 0, -47052, 0, 0, -45772, 0, -35816, 0, 0, 22848, 0, -7032, 0, 0, 26904, 0, 12992, 0, 0, -6796, 0, -36240, 0, 0, 61126, 0, -5032, 0, 0, -50424, 0, -5400, 0, 0, -70504, 0, 107648, 0, 0, -57792, 0, 48588, 0, 0, 24192, 0, 5896, 0, 0, -10440, 0, 4480, 0, 0, 23040, 0, -83148, 0, 0, 5280, 0, 65232, 0, 0, 30236, 0, 30432, 0, 0, -32856, 0, -16044, 0, 0, 79344, 0, 33984, 0, 0, 62622, 0, 132480, 0, 0, -87552, 0, 20496, 0, 0, -45132, 0, -6440, 0, 0, -9792, 0, -57276, 0, 0, -7744, 0, -59856, 0, 0, 876, 0, -60896, 0, 0, 8352, 0, 19312, 0, 0, -120176, 0, -43860, 0, 0, 9744, 0, 42336, 0, 0, 8180, 0, -61280, 0, 0, -121344, 0, -5568, 0, 0, 5016, 0, -46978, 0, 0, 4160, 0, -63936, 0, 0, -42112, 0, 6960, 0, 0, -18480, 0, 18144, 0, 0, 12296, 0, -153216, 0, 0, 7200, 0, 68532, 0, 0, -23232, 0, 56144, 0, 0, -41760, 0, -5792, 0, 0, -102432, 0, 57060, 0, 0, 1972, 0, -18648, 0, 0, -26432, 0, 17232, 0, 0, -77472, 0, 92904, 0, 0, 10320, 0, 10812, 0, 0, 15372, 0, -159744, 0, 0, 15540, 0, 54552, 0, 0, 24636, 0, -2372, 0, 0, 92912, 0, 143680, 0, 0, 10752, 0, -5376, 0, 0, -26052, 0, 102312, 0, 0, -61416, 0, -90132, 0, 0, 75680, 0, 56508, 0, 0, 35784, 0, -21312, 0, 0, 41992, 0, 46368, 0, 0, 70596, 0, 10656, 0, 0, 61488, 0, -414, 0, 0, -11236, 0, 80640, 0, 0, 31552, 0, -39624, 0, 0, -90312, 0, -15620, 0, 0, -37152, 0, -87764, 0, 0, -114912, 0, -3060, 0, 0, -17760, 0, -59000, 0, 0, 118944, 0, -12096, 0, 0, -9280, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "17.4.a.a", "char_is_minimal": false, "conrey_index": 324, "id": 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], [1, 0], [0, 3], [0, -8], [-1, 0], [0, 0], [24, 0], [0, 28], [0, 21], [-37, 0], [0, 0], [-24, 0], [0, 8], [0, -58], [-84, 0], [0, 0], [-71, 0], [0, -17], [0, -111], [-116, 0], [0, 0], [224, 0], [0, -72], [0, -60], [168, 0], [0, 0], [174, 0], [0, 80], [0, -28], [-30, 0], [0, 0], [-172, 0], [0, -45], [0, 192], [51, 0], [0, 0], [37, 0], [0, 58], [0, -348], [-464, 0], [0, 0], [-342, 0], [0, 672], [0, -148], [24, 0], [0, 0], [180, 0], [0, -288], [0, 568], [-441, 0], [0, 0], [-136, 0], [0, 58], [0, 318], [-240, 0], [0, 0], [-588, 0], [0, 928], [0, -90], [-252, 0], [0, 0], [110, 0], [0, -516], [0, -1036], [-433, 0], [0, 0], [-576, 0], [0, 484], [0, 17], [-480, 0], [0, 0], [-708, 0], [0, -777], [0, 362], [-174, 0], [0, 0], [116, 0], [0, -672], [0, -1392], [484, 0], [0, 0], [-359, 0], [0, -1026], [0, 756], [-224, 0], [0, 0], [444, 0], [0, 240], [0, -504], [774, 0], [0, 0], [1624, 0], [0, 60], [0, 1376], [864, 0], [0, 0], [-360, 0], [0, 382], [0, -1323], [888, 0], [0, 0]]}