# Stored data for newform 126.3.s.b, downloaded from the LMFDB on 25 April 2024.
{"label": "126.3.s.b", "space_label": "126.3.s", "level": 126, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504836628283518, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 1842893772545284786, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, 0, -2, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+2\\beta _{2}q^{4}+\\beta _{1}q^{5}+(5+3\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "s", "char_is_real": false, "Nk2": 1134, "analytic_conductor": 3.4332513309397408, "hecke_ring_index": 1, "level_radical": 42, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [126, 6, [29, 73], [3, 4]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [53, 107], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.700", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "86.210", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3144.164", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 0, 26], "traces": [0, 4, 0, 0, 4, 0, 0, 26, 0, 0, 4, 0, 0, 60, 0, 0, -8, 0, 0, 26, 0, 0, -40, 0, 0, -46, 0, 0, 8, 0, 0, -6, 0, 0, -64, 0, 0, -34, 0, 0, -8, 0, 0, -340, 0, 0, -64, 0, 0, 142, 0, 0, 60, 0, 0, -40, 0, 0, 64, 0, 0, 144, 0, 0, -32, 0, 0, -86, 0, 0, 8, 0, 0, 190, 0, 0, 104, 0, 0, -138, 0, 0, 228, 0, 0, -64, 0, 0, -40, 0, 0, 390, 0, 0, 204, 0, 0, 64, 0, 0, 92, 0, 0, 122, 0, 0, 192, 0, 0, 130, 0, 0, -88, 0, 0, -64, 0, 0, -512, 0, 0, -142, 0, 0, 12, 0, 0, -684, 0, 0, 60, 0, 0, 286, 0, 0, -64, 0, 0, -332, 0, 0, -148, 0, 0, 64, 0, 0, -136, 0, 0, -80, 0, 0, -260, 0, 0, -592, 0, 0, -32, 0, 0, -256, 0, 0, -172, 0, 0, 224, 0, 0, -340, 0, 0, -92, 0, 0, 384, 0, 0, 324, 0, 0, 128, 0, 0, 160, 0, 0, 104, 0, 0, 446, 0, 0, -92, 0, 0, 272, 0, 0, -392, 0, 0, 228, 0, 0, -120, 0, 0, 1088, 0, 0, 480, 0, 0, -12, 0, 0, -40, 0, 0, 992, 0, 0, 388, 0, 0, -866, 0, 0, 256, 0, 0, 204, 0, 0, -416, 0, 0, -316, 0, 0, 576, 0, 0, 390, 0, 0, 192, 0, 0, 640, 0, 0, -32, 0, 0, -374, 0, 0, -332, 0, 0, 192, 0, 0, 172, 0, 0, -432, 0, 0, 1216, 0, 0, -610, 0, 0, -88, 0, 0, -314, 0, 0, -600, 0, 0, -322, 0, 0, -380, 0, 0, -512, 0, 0, -288, 0, 0, -2210, 0, 0, 104, 0, 0, -44, 0, 0, 12, 0, 0, -1106, 0, 0, -552, 0, 0, 320, 0, 0, -128, 0, 0, -690, 0, 0, 912, 0, 0, 122, 0, 0, 172, 0, 0, 540, 0, 0, -64, 0, 0, 572, 0, 0, -320, 0, 0, -608, 0, 0, 80, 0, 0, -148, 0, 0, -168, 0, 0, 384, 0, 0, 120, 0, 0, -202, 0, 0, -136, 0, 0, 622, 0, 0, -408, 0, 0, 364, 0, 0, 180, 0, 0, -260, 0, 0, 64, 0, 0, 1024, 0, 0, -448, 0, 0, 558, 0, 0, 368, 0, 0, -90, 0, 0, 704, 0, 0, 446, 0, 0, 488, 0, 0, -172, 0, 0, -260, 0, 0, 612, 0, 0, 192, 0, 0, 1584, 0, 0, -340, 0, 0, 548, 0, 0, -260, 0, 0, 1200, 0, 0, -960, 0, 0, 384, 0, 0, -208, 0, 0, 1140, 0, 0, 936, 0, 0, 478, 0, 0, 128, 0, 0, 844, 0, 0, 644, 0, 0, -172, 0, 0, -512, 0, 0, -1196, 0, 0, -972, 0, 0, -510, 0, 0, -568, 0, 0, -838, 0, 0, -92, 0, 0, 512, 0, 0, 48, 0, 0, -374, 0, 0, 672, 0, 0, -392, 0, 0, -684, 0, 0, 380, 0, 0, 900, 0, 0, -2040, 0, 0, -120, 0, 0, 1622, 0, 0, -960, 0, 0, -34, 0, 0, 676, 0, 0, 480, 0, 0, -2744, 0, 0, 690, 0, 0, 128, 0, 0, -3456, 0, 0, 460, 0, 0, -1518, 0, 0, -332, 0, 0, -5100, 0, 0, -64, 0, 0, 388, 0, 0, -592, 0, 0, -954, 0, 0, 2508, 0, 0, 526, 0, 0, 256, 0, 0, -480, 0, 0, -288, 0, 0, -156, 0, 0, -136, 0, 0, -416, 0, 0, -960, 0, 0, 1532, 0, 0, 160, 0, 0, 1530, 0, 0, 576, 0, 0, -816, 0, 0, -80, 0, 0, 1894, 0, 0, 2968, 0, 0, -958, 0, 0, 1184, 0, 0, -3040, 0, 0, -384, 0, 0, 2130, 0, 0, -32, 0, 0, -76, 0, 0, -416, 0, 0, 1280, 0, 0, -1024, 0, 0, -332, 0, 0, 408, 0, 0, 802, 0, 0, -688, 0, 0, -1024, 0, 0, 172, 0, 0, 2660, 0, 0, 224, 0, 0, 416, 0, 0, 60, 0, 0, 1216, 0, 0, 680, 0, 0, -442, 0, 0, 576, 0, 0, 1824, 0, 0, 1012, 0, 0, 442, 0, 0, 2184, 0, 0, 656, 0, 0, -768, 0, 0, -600, 0, 0, -128, 0, 0, 1342, 0, 0, 324, 0, 0, 4276, 0, 0, -380, 0, 0, -990, 0, 0, 512, 0, 0, -906, 0, 0, 1248, 0, 0, -288, 0, 0, 640, 0, 0, 678, 0, 0, 960, 0, 0, 792, 0, 0, 104, 0, 0, 260, 0, 0, -928, 0, 0, -3716, 0, 0, -892, 0, 0, -138, 0, 0, -3896, 0, 0, -740, 0, 0, -752, 0, 0, -180, 0, 0, -552, 0, 0, 2160, 0, 0, -544, 0, 0, -3264, 0, 0, 0, 0, 0, -128, 0, 0, -392, 0, 0, -2216, 0, 0, 340, 0, 0, -2210, 0, 0, 912, 0, 0, -1712, 0, 0, -3328, 0, 0, -2078, 0, 0, -480, 0, 0, 172, 0, 0, -1644, 0, 0, 1316, 0, 0, 1088, 0, 0, -1562, 0, 0, 736, 0, 0, 5852, 0, 0, -960, 0, 0, 2924, 0, 0, -792, 0, 0, -320, 0, 0, 132, 0, 0, -1290, 0, 0, -1664, 0, 0, -2960, 0, 0, 80, 0, 0, -460, 0, 0, -1792, 0, 0, -4446, 0, 0, 992, 0, 0, -168, 0, 0, 1084, 0, 0, -768, 0, 0, 1552, 0, 0, 1002, 0, 0, 120, 0, 0, -860, 0, 0, -3464, 0, 0, 1306, 0, 0, -1280, 0, 0, 1564, 0, 0, 256, 0, 0, 2444, 0, 0, -884, 0, 0, 3044, 0, 0, -408, 0, 0, -3648, 0, 0, 3400, 0, 0, 2850, 0, 0, -128, 0, 0, 180, 0, 0, 3968, 0, 0, 1904, 0, 0, 632, 0, 0, 4652, 0, 0, 64, 0, 0, -2158, 0, 0, 576, 0, 0, -3840, 0, 0, 480, 0, 0, -448, 0, 0, 1560, 0, 0, 1946, 0, 0, -1628, 0, 0, 158, 0, 0, 768], "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, 3, 2, -1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 21, 8, -1, 6, 0]], "char_orbit_index": 19, "prim_orbit_index": 8, "minimal_twist": "126.3.s.b", "char_is_minimal": true, "conrey_index": 53, "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, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 1, 0, 0], [0, 0, 0, 0], [5, 0, 3, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 2, 0], [0, -5, 0, 5], [0, 0, 0, 0], [15, 0, 0, 0], [0, 5, 0, 3], [0, 0, 0, 0], [-4, 0, 4, 0], [0, -8, 0, 8], [0, 0, 0, 0], [13, 0, -13, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-10, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, -23, 0], [0, 15, 0, 0], [0, 0, 0, 0], [-6, 0, 16, 0], [0, 0, 0, -16], [0, 0, 0, 0], [0, 0, -3, 0], [0, -4, 0, 4], [0, 0, 0, 0], [-16, 0, 0, 0], [0, 5, 0, 3], [0, 0, 0, 0], [-17, 0, 17, 0], [0, 13, 0, -13], [0, 0, 0, 0], [-4, 0, 4, 0], [0, 0, 0, -57], [0, 0, 0, 0], [-85, 0, 0, 0], [0, -10, 0, 0], [0, 0, 0, 0], [0, 0, -32, 0], [0, 51, 0, 0], [0, 0, 0, 0], [16, 0, 39, 0], [0, 0, 0, -23], [0, 0, 0, 0], [0, 0, 30, 0], [0, 24, 0, -24], [0, 0, 0, 0], [-10, 0, 0, 0], [0, -6, 0, 16], [0, 0, 0, 0], [32, 0, -32, 0], [0, -64, 0, 64], [0, 0, 0, 0], [72, 0, -72, 0], [0, 0, 0, -3], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 15, 0, 0], [0, 0, 0, 0], [0, 0, -43, 0], [0, -16, 0, 0], [0, 0, 0, 0], [-6, 0, 16, 0], [0, 0, 0, 37], [0, 0, 0, 0], [0, 0, 95, 0], [0, -17, 0, 17], [0, 0, 0, 0], [26, 0, 0, 0], [0, -40, 0, 25], [0, 0, 0, 0], [-69, 0, 69, 0], [0, -4, 0, 4], [0, 0, 0, 0], [114, 0, -114, 0], [0, 0, 0, 43], [0, 0, 0, 0], [-16, 0, 0, 0], [0, -85, 0, 0], [0, 0, 0, 0], [0, 0, -20, 0], [0, 96, 0, 0], [0, 0, 0, 0], [75, 0, 45, 0], [0, 0, 0, -32], [0, 0, 0, 0], [0, 0, 102, 0], [0, 13, 0, -13], [0, 0, 0, 0], [16, 0, 0, 0], [0, 16, 0, 39], [0, 0, 0, 0], [46, 0, -46, 0]]}