# Stored data for newform 128.4.a.d, downloaded from the LMFDB on 19 April 2024. {"label": "128.4.a.d", "space_label": "128.4.a", "level": 128, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220480, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1286841848865643763, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-2, 1]], [5, [-6, 1]]], "qexp_display": "q+2q^{3}+6q^{5}+20q^{7}-23q^{9}+14q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2048, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 7.552244480734799, "hecke_ring_index": 1, "level_radical": 2, "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": [128, 1, [127, 5], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "0.995", "prec": 17}, {"__RealLiteral__": 0, "data": "0.073", "prec": 17}, {"__RealLiteral__": 0, "data": "1.975", "prec": 17}, {"__RealLiteral__": 0, "data": "0.214", "prec": 17}, {"__RealLiteral__": 0, "data": "4.868", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1]], "trace_display": [0, 2, 6, 20], "traces": [0, 1, 0, 2, 0, 6, 0, 20, 0, -23, 0, 14, 0, 54, 0, 12, 0, -66, 0, 162, 0, 40, 0, 172, 0, -89, 0, -100, 0, -2, 0, -128, 0, 28, 0, 120, 0, 158, 0, 108, 0, 202, 0, -298, 0, -138, 0, -408, 0, 57, 0, -132, 0, -690, 0, 84, 0, 324, 0, -322, 0, -298, 0, -460, 0, 324, 0, 202, 0, 344, 0, -700, 0, -418, 0, -178, 0, 280, 0, 744, 0, 421, 0, -678, 0, -396, 0, -4, 0, -82, 0, 1080, 0, -256, 0, 972, 0, -1122, 0, -322, 0, 1390, 0, 788, 0, 240, 0, 1614, 0, 2014, 0, 316, 0, -542, 0, 1032, 0, -1242, 0, -1320, 0, -1135, 0, 404, 0, -1284, 0, 1712, 0, -596, 0, -2118, 0, 3240, 0, -600, 0, -486, 0, 1286, 0, -816, 0, 756, 0, -12, 0, 114, 0, -2666, 0, 172, 0, 1518, 0, -768, 0, 838, 0, -1380, 0, 3440, 0, 1346, 0, 168, 0, -1052, 0, 719, 0, -3726, 0, 38, 0, -1780, 0, -644, 0, -2790, 0, -3418, 0, -596, 0, 948, 0, -924, 0, -2000, 0, -1968, 0, -1058, 0, 648, 0, 726, 0, 4116, 0, 404, 0, -40, 0, 1212, 0, -3956, 0, 2268, 0, 1482, 0, -1400, 0, -1788, 0, -2560, 0, -836, 0, -3564, 0, -896, 0, 2047, 0, 3410, 0, 4502, 0, 560, 0, 2302, 0, -2448, 0, 1488, 0, 4024, 0, -3586, 0, 3542, 0, 342, 0, 8748, 0, -1356, 0, -1250, 0, 2408, 0, -792, 0, -6638, 0, 3160, 0, 46, 0, -1724, 0, -4140, 0, -164, 0, 4814, 0, -1640, 0, 2160, 0, -1246, 0, 3982, 0, 2944, 0, 4126, 0, 3446, 0, 1944, 0, 4040, 0, -557, 0, -2244, 0, -1514, 0, -1932, 0, -1400, 0, 9288, 0, -5960, 0, 2780, 0, -1788, 0, 5490, 0, 1576, 0, -5556, 0, -2054, 0, -2760, 0, 2494, 0, -28, 0, 3228, 0, -10692, 0, -4806, 0, 4028, 0, -8160, 0, -2914, 0, -3634, 0, 1212, 0, 7186, 0, -1084, 0, -1792, 0, -5720, 0, 2064, 0, 4446, 0, 430, 0, -5400, 0, 850, 0, -4200, 0, -2640, 0, -10988, 0, 19385, 0, -2270, 0, -2508, 0, 872, 0, -4646, 0, -13800, 0, 3454, 0, -2568, 0, -108, 0, -1490, 0, 3424, 0, 10240, 0, 1680, 0, 6854, 0, -7458, 0, -11352, 0, -4236, 0, 4464, 0, -4706, 0, 6480, 0, 5598, 0, -6912, 0, 2526, 0, 2212, 0, -838, 0, -972, 0, -6440, 0, -4068, 0, 2572, 0, 26, 0, -15578, 0, 9384, 0, 5874, 0, -5960, 0, 1512, 0, -6792, 0, -9314, 0, -24, 0, 27864, 0, -3828, 0, -1311, 0, 15414, 0, -492, 0, -5332, 0, -3650, 0, 2828, 0, 344, 0, 6480, 0, -15862, 0, 6600, 0, 78, 0, -4376, 0, -1536, 0, 13714, 0, 4040, 0, 1676, 0, -4172, 0, -14418, 0, 15870, 0, 19072, 0, 8532, 0, 6880, 0, -6732, 0, 19428, 0, 2692, 0, -2490, 0, 132, 0, -1932, 0, -14000, 0, 2826, 0, -2104, 0, 2268, 0, 8340, 0, 1438, 0, 10534, 0, -8360, 0, -16200, 0, 4728, 0, -5712, 0, 76, 0, -9478, 0, -5858, 0, -3560, 0, 8448, 0, 17417, 0, 7406, 0, 10908, 0, 9684, 0, -5580, 0, 798, 0, 1910, 0, -6836, 0, 12084, 0, 1754, 0, 6854, 0, -324, 0, 14880, 0, 1896, 0, 2294, 0, -16092, 0, -1848, 0, 16242, 0, -3252, 0, 8420, 0, -15990, 0, -21674, 0, -3936, 0, -15308, 0, -12542, 0, -2116, 0, -13560, 0, -9660, 0, -7452, 0, -18578, 0, -20736, 0, 1452, 0, 14514, 0, -7920, 0, 8232, 0, -3460, 0, 20686, 0, -4646, 0, -6810, 0, -9776, 0, -80, 0, -22032, 0, -8794, 0, 2424, 0, 16398, 0, 21374, 0, -17200, 0, -1640, 0, 3421, 0, 4536, 0, -10428, 0, -18916, 0, 2964, 0, 10272, 0, 3078, 0, 16100, 0, -5250, 0, -4502, 0, -3576, 0, 11076, 0, -4508, 0, -5120, 0, 30766, 0, -12708, 0, 9614, 0, -20518, 0, 70, 0, -7128, 0, 19440, 0, -344, 0, -1792, 0, -4172, 0, 23070, 0, 8900, 0, 2622, 0, -22440, 0, 6820, 0, -14682, 0, -2916, 0, 9004, 0, -37260, 0, -23270, 0, -6440, 0, 7716, 0, -13332, 0, 4604, 0, -31530, 0, 25596, 0, -4896, 0, 27800, 0, 22014, 0, -17112, 0, -22016, 0, 4536, 0, 8048, 0, 19016, 0, 15760, 0, -7172, 0, 178, 0, 15996, 0, -4283, 0, 19668, 0, 10622, 0, 684, 0, 2828, 0, -8878, 0, 17496, 0, -21852, 0, -15996, 0, 15594, 0, 32280, 0, 32024, 0, -2500, 0, 1032, 0, -26602, 0, 4816, 0, -13958, 0, 40280, 0, 9108, 0, -17388, 0, -11970, 0, -13276, 0, 12318, 0, 11392, 0, 6320, 0, 32724, 0, -9800, 0, 200, 0, 5028, 0, 26698, 0, -3448, 0, -10840, 0, -16092, 0, -8280, 0, -4794, 0, 26928, 0, 1886, 0, -5852, 0, 20640, 0, 9628, 0, 39114, 0, -1090, 0, -3280, 0, 8076, 0, -48276, 0, -24840, 0, -9730, 0, 1100, 0, -2492, 0, -38074, 0, 24230, 0, 7964, 0, -3762, 0, -6312, 0, 12800, 0, 16820, 0, -24385, 0, 8252, 0, 4314, 0, -22700, 0, 6892, 0, 27176, 0, -22162, 0, -22356, 0, -8790, 0, 10558, 0, 8080, 0, -7392, 0, 228, 0, -1114, 0, 10416, 0, 10908, 0, 25806, 0, -25680, 0, 6574, 0, -3028, 0, 47154, 0, 642, 0, -3864, 0, 23308, 0, 34240, 0, 5894, 0, -66096, 0, -16740, 0, 18576, 0, 256, 0, 45540, 0, -11920, 0, -20508, 0, -21450, 0, -31970, 0, -40904, 0, -9492, 0, -3576, 0, -42360, 0, -27380, 0, 10980, 0, -37800, 0, -14062, 0, -18124, 0, 10302, 0, 9234, 0, -11112, 0, -5544, 0, 5054, 0, -4108, 0, 30462, 0, 34744, 0, -12000, 0, 32082, 0, -22572, 0, 4988, 0, 12970, 0, -11808, 0, -56, 0, -9720, 0, -13407, 0, -37122, 0, -6348, 0, 1652, 0, -21384, 0, -24650, 0, 25720, 0, -9612, 0, 23646, 0, -1148, 0, -46322, 0, 38108, 0, 4356, 0, -16320, 0, -51256, 0, -18640, 0, -5828, 0, 24696, 0, 29022, 0, -15800, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "128.4.a.a", "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], [1], [0], [2], [0], [6], [0], [20], [0], [-23], [0], [14], [0], [54], [0], [12], [0], [-66], [0], [162], [0], [40], [0], [172], [0], [-89], [0], [-100], [0], [-2], [0], [-128], [0], [28], [0], [120], [0], [158], [0], [108], [0], [202], [0], [-298], [0], [-138], [0], [-408], [0], [57], [0], [-132], [0], [-690], [0], [84], [0], [324], [0], [-322], [0], [-298], [0], [-460], [0], [324], [0], [202], [0], [344], [0], [-700], [0], [-418], [0], [-178], [0], [280], [0], [744], [0], [421], [0], [-678], [0], [-396], [0], [-4], [0], [-82], [0], [1080], [0], [-256], [0], [972], [0], [-1122], [0], [-322], [0]]}