# Stored data for newform 8.5.d.a, downloaded from the LMFDB on 13 May 2024.
{"label": "8.5.d.a", "space_label": "8.5.d", "level": 8, "weight": 5, "hecke_orbit": 1, "hecke_orbit_code": 206242316296, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1369284050751797824, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [14, 1]]], "qexp_display": "q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 200, "analytic_conductor": 0.8269597046707546, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [8, 2, [7, 5], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [3], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.967", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.882", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.556", "prec": 17}], "related_objects": [], "self_twist_discs": [-8], "cm_discs": [-8], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "4.2.1.d2", "trace_display": [4, -14, 0, 0], "traces": [0, 1, 4, -14, 16, 0, -56, 0, 64, 115, 0, -46, -224, 0, 0, 0, 256, -574, 460, 434, 0, 0, -184, 0, -896, 625, 0, -476, 0, 0, 0, 0, 1024, 644, -2296, 0, 1840, 0, 1736, 0, 0, -1246, 0, -3502, -736, 0, 0, 0, -3584, 2401, 2500, 8036, 0, 0, -1904, 0, 0, -6076, 0, -238, 0, 0, 0, 0, 4096, 0, 2576, -5134, -9184, 0, 0, 0, 7360, 9506, 0, -8750, 6944, 0, 0, 0, 0, -2651, -4984, 11186, 0, 0, -14008, 0, -2944, 5474, 0, 0, 0, 0, 0, 0, -14336, -9982, 9604, -5290, 10000, 0, 32144, 0, 0, 0, 0, 8786, -7616, 0, 0, 0, 0, -15934, -24304, 0, 0, 0, -952, 0, 0, -12525, 0, 17444, 0, 0, 0, 0, 16384, 49028, 0, -30478, 10304, 0, -20536, 0, -36736, 19106, 0, 3794, 0, 0, 0, 0, 29440, 0, 38024, -33614, 0, 0, -35000, 0, 27776, -66010, 0, 0, 0, 0, 0, 0, 0, 0, -10604, 50546, -19936, 0, 44744, 0, 0, 28561, 0, 49910, -56032, 0, 0, 0, -11776, 3332, 21896, -62926, 0, 0, 0, 0, 0, 0, 0, 26404, 0, 0, 0, 0, -57344, -64894, -39928, 0, 38416, 0, -21160, 0, 40000, 71876, 0, 0, 128576, 0, 0, 0, 0, -19964, 0, -37966, 0, 0, 35144, 0, -30464, 0, 0, -133084, 0, 0, 0, 0, 0, 71875, -63736, 95858, -97216, 0, 0, 0, 0, 79778, 0, 0, -3808, 0, 0, 0, 0, -78526, -50100, 75670, 0, 0, 69776, 0, 0, -156604, 0, 91154, 0, 0, 0, 0, 65536, 16898, 196112, 0, 0, 0, -121912, 0, 41216, 0, 0, -76636, -82144, 0, 0, 0, -146944, 0, 76424, -28750, 0, 0, 15176, 0, 0, -101278, 0, -153454, 0, 0, 0, 0, 117760, 245955, 0, 139748, 152096, 0, -134456, 0, 0, 21896, 0, 0, -140000, 0, 0, 0, 111104, 0, -264040, 105266, 0, 0, 0, 0, 0, 80738, 0, 0, 0, 0, 0, 0, 0, -123004, 0, -249116, -42416, 0, 202184, 0, -79744, 0, 0, -218926, 178976, 0, 0, 0, 0, 1346, 114244, 223076, 0, 0, 199640, 0, -224128, 0, 0, 192146, 0, 0, 0, 0, -47104, -211582, 13328, 0, 87584, 0, -251704, 0, 0, 58035, 0, 175350, 0, 0, 0, 0, 0, -143290, 0, 0, 0, 0, 105616, 0, 0, 0, 0, 183314, 0, 0, 0, 0, -229376, 0, -259576, -402730, -159712, 0, 0, 0, 153664, 426692, 0, 0, -84640, 0, 0, 0, 160000, 265154, 287504, 0, 0, 0, 0, 0, 514304, -223006, 0, -267484, 0, 0, 0, 0, 0, -53116, -79856, -86926, 0, 0, -151864, 0, 0, -358750, 0, 0, 140576, 0, 0, 0, -121856, -40894, 0, 0, 0, 0, -532336, 0, 0, 276115, 0, 378386, 0, 0, 0, 0, 0, 346754, 287500, 57316, -254944, 0, 383432, 0, -388864, -361054, 0, 273224, 0, 0, 0, 0, 0, 0, 319112, -435022, 0, 0, 0, 0, -15232, 161092, 0, 271250, 0, 0, 0, 0, 0, 0, -314104, 0, -200400, 0, 302680, 0, 0, -707644, 0, 129362, 279104, 0, 0, 0, 0, 0, -626416, 145202, 0, 0, 364616, 0, 0, 0, 0, -399854, 0, 0, 0, 0, 262144, -206584, 67592, 0, 784448, 0, 0, 0, 0, 469154, 0, -388654, -487648, 0, 0, 0, 164864, 279841, 0, -27370, 0, 0, -306544, 0, -328576, 880964, 0, -110446, 0, 0, 0, 0, -587776, 0, 0, 446066, 305696, 0, -115000, 0, 0, 0, 0, 0, 60704, 0, 0, 0, 0, -369656, -405112, -582862, 0, 0, -613816, 0, 0, -255646, 0, -219118, 0, 0, 0, 0, 471040, -665854, 983820, 908516, 0, 0, 558992, 0, 608384, 0, 0, 605906, -537824, 0, 0, 0, 0, 39746, 87584, 0, 0, 0, 0, 0, -560000, 112994, 0, -590410, 0, 0, 0, 0, 444416, 0, 0, 0, -1056160, 0, 421064, 0, 0, -649822, 0, -450478, 0, 0, 0, 0, 0, 390625, 322952, 279496, 0, 0, 0, 0, 0, 531524, 0, 0, 0, 0, 0, 0, 0, -589438, -492016, 646898, 0, 0, -996464, 0, -169664, 10948, 0, 0, 808736, 0, 0, 0, -318976, 1093190, 0, 119474, 0, 0, -875704, 0, 715904, 0, 0, 0, 0, 0, 0, 0, 0, 646658, 5384, -297500, 456976, 0, 892304, 0, 0, -1342012, 0, -774574, 798560, 0, 0, 0, -896512, 0, 0, -416206, 0, 0, 768584, 0, 0, 715204, 0, -1116892, 0, 0, 0, 0, -188416, 0, -846328, 0, 53312, 0, 0, 0, 350336, 0, 0, 0, -1006816, 0, 0, 0, 0, 0, 232140, 1099364, 0, 0, 701400, 0, 0, -844649, 0, 2010148, 0, 0, 0, 0, 0, 236164, -573160, -988558, 0, 0, 0, 0, 0, 0, 0, 1286390, 422464, 0, 0, 0, 0, -1276156, 0, 0, 0, 0, 733256, 0, 0, 784994, 0, 0, 0, 0, 0, 0, -917504, -71806, 0, -236572, -1038304, 0, -1610920, 0, -638848, 0, 0, -540764, 0, 0, 0, 0, 614656, 0, 1706768, -381262, 0, 0, 0, 0, -338560, 0, 0, 0, 0, 0, 0, 0, 640000, 629510, 1060616, -437276, 1150016, 0, 0, 0, 0, 1193762, 0, -1283758, 0, 0, 0, 0, 2057216, -1519868, -892024, 0, 0, 0, -1069936, 0, 0, 402500, 0, 224786, 0, 0, 0, 0, 0, -1378174, -212464, 0, -319424, 0, -347704, 0, 0, 707281, 0, 1417892, -607456, 0, 0, 0, 0, 2148356, -1435000, 0, 0, 0, 0, 0, 562304, -24094, 0, 1233554, 0, 0, 0, 0, -487424, 0, -163576, -3443370, 0, 0, 0, 0, 0, -1147930, 0, 0, -2129344, 0, 0, 0, 0, 515522, 1104460, 1545266, 0, 0, 1513544, 0, 0, 0, 0, 121946, 0, 0, 0, 0, 0, 0, 1387016, 0, 1150000, 0, 229264, 0, -1019776, 0, 0, 1292498, 1533728, 0, 0, 0, -1555456, -514556, -1444216, 0, 0, 0, 1092896, 0, 0, -1473724, 0, 0, 0, 0, 0, 0, 0, -606718, 0, 1042034, 1276448, 0, -1740088, 0, 0, -1240414, 0, -1130332, 0, 0, 0, 0, -60928, 0, 644368, -805582, 0, 0, 1085000, 0, 0, -1796254, 0, 0, 0, 0, 0, 0, 0, 923521, 0, 1010390, -1256416, 0, 0, 0, -801600, 3487624, 0, -937006, 1210720, 0, 0, 0, 0, 1769666, -2830576, -251804, 0, 0, 517448, 0, 1116416, 0, 0, 0, 0, 0, 0, 0, 0, 3064964, 0, 0, -2505664, 0, 580808, 0, 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], [1, 1, 8, 4, -1, 2, -8]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "8.5.d.a", "char_is_minimal": true, "conrey_index": 3, "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], [1], [4], [-14], [16], [0], [-56], [0], [64], [115], [0], [-46], [-224], [0], [0], [0], [256], [-574], [460], [434], [0], [0], [-184], [0], [-896], [625], [0], [-476], [0], [0], [0], [0], [1024], [644], [-2296], [0], [1840], [0], [1736], [0], [0], [-1246], [0], [-3502], [-736], [0], [0], [0], [-3584], [2401], [2500], [8036], [0], [0], [-1904], [0], [0], [-6076], [0], [-238], [0], [0], [0], [0], [4096], [0], [2576], [-5134], [-9184], [0], [0], [0], [7360], [9506], [0], [-8750], [6944], [0], [0], [0], [0], [-2651], [-4984], [11186], [0], [0], [-14008], [0], [-2944], [5474], [0], [0], [0], [0], [0], [0], [-14336], [-9982], [9604], [-5290], [10000]]}