# Stored data for newform 8.3.d.a, downloaded from the LMFDB on 23 April 2024.
{"label": "8.3.d.a", "space_label": "8.3.d", "level": 8, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 206208761864, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1911721951462934128, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 72, "analytic_conductor": 0.21798421148823752, "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": "2.860", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.423", "prec": 17}], "related_objects": [], "self_twist_discs": [-8], "cm_discs": [-8], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.1.d2", "trace_display": [-2, -2, 0, 0], "traces": [0, 1, -2, -2, 4, 0, 4, 0, -8, -5, 0, 14, -8, 0, 0, 0, 16, 2, 10, -34, 0, 0, -28, 0, 16, 25, 0, 28, 0, 0, 0, 0, -32, -28, -4, 0, -20, 0, 68, 0, 0, -46, 0, 14, 56, 0, 0, 0, -32, 49, -50, -4, 0, 0, -56, 0, 0, 68, 0, -82, 0, 0, 0, 0, 64, 0, 56, 62, 8, 0, 0, 0, 40, -142, 0, -50, -136, 0, 0, 0, 0, -11, 92, 158, 0, 0, -28, 0, -112, 146, 0, 0, 0, 0, 0, 0, 64, -94, -98, -70, 100, 0, 8, 0, 0, 0, 0, -178, 112, 0, 0, 0, 0, 98, -136, 0, 0, 0, 164, 0, 0, 75, 0, 92, 0, 0, 0, 0, -128, -28, 0, 62, -112, 0, -124, 0, -16, -238, 0, 206, 0, 0, 0, 0, -80, 0, 284, -98, 0, 0, 100, 0, 272, -10, 0, 0, 0, 0, 0, 0, 0, 0, 22, -322, -184, 0, -316, 0, 0, 169, 0, 170, 56, 0, 0, 0, 224, 164, -292, -34, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, -128, 98, 188, 0, 196, 0, 140, 0, -200, -124, 0, 0, -16, 0, 0, 0, 0, -476, 0, -226, 0, 0, 356, 0, -224, 0, 0, 284, 0, 0, 0, 0, 0, -125, -196, 446, 272, 0, 0, 0, 0, 434, 0, 0, -328, 0, 0, 0, 0, 194, -150, -230, 0, 0, -184, 0, 0, -316, 0, -466, 0, 0, 0, 0, 256, 386, 56, 0, 0, 0, -124, 0, 224, 0, 0, -292, 248, 0, 0, 0, 32, 0, 476, 350, 0, 0, -412, 0, 0, -238, 0, -82, 0, 0, 0, 0, 160, -285, 0, 188, -568, 0, 196, 0, 0, 392, 0, 0, -200, 0, 0, 0, -544, 0, 20, 542, 0, 0, 0, 0, 0, -526, 0, 0, 0, 0, 0, 0, 0, 356, 0, -68, -44, 0, 644, 0, 368, 0, 0, 14, 632, 0, 0, 0, 0, -478, -338, -196, 0, 0, -340, 0, -112, 0, 0, -658, 0, 0, 0, 0, -448, 194, -328, 0, 584, 0, 68, 0, 0, 795, 0, -150, 0, 0, 0, 0, 0, 230, 0, 0, 0, 0, -56, 0, 0, 0, 0, 686, 0, 0, 0, 0, 256, 0, -196, -70, -376, 0, 0, 0, -392, -124, 0, 0, -280, 0, 0, 0, 400, -766, 248, 0, 0, 0, 0, 0, 32, -334, 0, 476, 0, 0, 0, 0, 0, -412, 952, -514, 0, 0, 452, 0, 0, 50, 0, 0, -712, 0, 0, 0, 448, 578, 0, 0, 0, 0, -568, 0, 0, -245, 0, 878, 0, 0, 0, 0, 0, 866, 250, -644, 392, 0, -892, 0, -544, -238, 0, 56, 0, 0, 0, 0, 0, 0, -868, -34, 0, 0, 0, 0, 656, 196, 0, -850, 0, 0, 0, 0, 0, 0, -388, 0, 300, 0, 460, 0, 0, 644, 0, 782, 368, 0, 0, 0, 0, 0, 632, -802, 0, 0, 932, 0, 0, 0, 0, -338, 0, 0, 0, 0, -512, -952, -772, 0, -112, 0, 0, 0, 0, -1006, 0, 398, 248, 0, 0, 0, -448, 529, 0, 410, 0, 0, 584, 0, -496, 68, 0, 686, 0, 0, 0, 0, -64, 0, 0, 1022, -952, 0, -700, 0, 0, 0, 0, 0, 824, 0, 0, 0, 0, -56, 476, -226, 0, 0, 164, 0, 0, 626, 0, -658, 0, 0, 0, 0, -320, 2, 570, -196, 0, 0, -376, 0, 1136, 0, 0, -1138, -392, 0, 0, 0, 0, -862, -784, 0, 0, 0, 0, 0, 400, 914, 0, -310, 0, 0, 0, 0, 1088, 0, 0, 0, -40, 0, -1084, 0, 0, -334, 0, -562, 0, 0, 0, 0, 0, 625, 1052, 952, 0, 0, 0, 0, 0, 452, 0, 0, 0, 0, 0, 0, 0, 482, -712, 1214, 0, 0, 136, 0, 88, -1148, 0, 0, -1288, 0, 0, 0, -736, 710, 0, -994, 0, 0, -28, 0, -1264, 0, 0, 0, 0, 0, 0, 0, 0, -1246, 956, 700, 676, 0, 392, 0, 0, -892, 0, 398, 680, 0, 0, 0, 224, 0, 0, 734, 0, 0, 1316, 0, 0, -92, 0, -868, 0, 0, 0, 0, 896, 0, -388, 0, 656, 0, 0, 0, -1168, 0, 0, 0, -136, 0, 0, 0, 0, 0, -1590, -388, 0, 0, 300, 0, 0, 559, 0, 28, 0, 0, 0, 0, 0, 868, -460, -322, 0, 0, 0, 0, 0, 0, 0, -790, 112, 0, 0, 0, 0, 932, 0, 0, 0, 0, -1372, 0, 0, 1394, 0, 0, 0, 0, 0, 0, -512, -1054, 0, -772, 392, 0, 140, 0, 752, 0, 0, 1564, 0, 0, 0, 0, 784, 0, 248, 926, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, -800, -730, 1532, -1988, -496, 0, 0, 0, 0, -1582, 0, -178, 0, 0, 0, 0, -64, -476, 668, 0, 0, 0, -952, 0, 0, -700, 0, 1262, 0, 0, 0, 0, 0, 98, 824, 0, -1904, 0, 1028, 0, 0, 841, 0, 476, -904, 0, 0, 0, 0, 164, -100, 0, 0, 0, 0, 0, 1424, 1202, 0, 1646, 0, 0, 0, 0, -896, 0, -1156, 570, 0, 0, 0, 0, 0, 470, 0, 0, 1136, 0, 0, 0, 0, -1438, 490, -1762, 0, 0, -1756, 0, 0, 0, 0, -154, 0, 0, 0, 0, 0, 0, -1732, 0, -500, 0, 1288, 0, -784, 0, 0, -1714, 1784, 0, 0, 0, 1088, 2212, 476, 0, 0, 0, -112, 0, 0, -1084, 0, 0, 0, 0, 0, 0, 0, 1058, 0, -1666, 1736, 0, 68, 0, 0, -718, 0, 1052, 0, 0, 0, 0, -1312, 0, -392, -994, 0, 0, 1700, 0, 0, -142, 0, 0, 0, 0, 0, 0, 0, 961, 0, 890, 776, 0, 0, 0, -600, 136, 0, 974, -920, 0, 0, 0, 0, -1918, -1288, 2044, 0, 0, -1564, 0, -736, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -1264, 0, 1604, 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": "8.3.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], [-2], [-2], [4], [0], [4], [0], [-8], [-5], [0], [14], [-8], [0], [0], [0], [16], [2], [10], [-34], [0], [0], [-28], [0], [16], [25], [0], [28], [0], [0], [0], [0], [-32], [-28], [-4], [0], [-20], [0], [68], [0], [0], [-46], [0], [14], [56], [0], [0], [0], [-32], [49], [-50], [-4], [0], [0], [-56], [0], [0], [68], [0], [-82], [0], [0], [0], [0], [64], [0], [56], [62], [8], [0], [0], [0], [40], [-142], [0], [-50], [-136], [0], [0], [0], [0], [-11], [92], [158], [0], [0], [-28], [0], [-112], [146], [0], [0], [0], [0], [0], [0], [64], [-94], [-98], [-70], [100]]}