# Stored data for newform 200.4.d.a, downloaded from the LMFDB on 25 April 2024. {"label": "200.4.d.a", "space_label": "200.4.d", "level": 200, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 206225539272, "dim": 2, "is_polredabs": true, "nf_label": "2.0.7.1", "trace_hash": 724738366384683975, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [28, 0, 1]], [7, [-8, 1]]], "qexp_display": "q+(1+\\beta )q^{2}-2\\beta q^{3}+(-6+2\\beta )q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 3200, "analytic_conductor": 11.800382001148122, "hecke_ring_index": 2, "level_radical": 10, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [200, 2, [151, 101, 177], [2, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [101], "field_disc": -7, "field_disc_factorization": [[-1, 1], [7, 1]], "field_poly": [2, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.930", "prec": 17}, {"__RealLiteral__": 0, "data": "0.079", "prec": 17}, {"__RealLiteral__": 0, "data": "14.916", "prec": 20}, {"__RealLiteral__": 0, "data": "2.038", "prec": 17}, {"__RealLiteral__": 0, "data": "145.243", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [2, 0, 0, 16], "traces": [0, 2, 2, 0, -12, 0, 28, 16, -40, -2, 0, 0, 56, 0, 16, 0, 16, 28, -2, 0, 0, 0, 84, 304, -112, 0, 280, 0, -96, 0, 0, 448, 352, -168, 28, 0, 12, 0, 196, -560, 0, -140, 224, 0, 168, 0, 304, -672, -672, -558, 0, 0, 560, 0, 728, 0, -320, -392, 840, 0, 0, 0, 448, -16, 576, 0, -168, 0, -168, 0, 0, -144, 40, 588, 1288, 0, 392, 0, -560, -928, 0, -1510, -140, 0, 448, 0, -2324, -1680, -336, 532, 0, 0, -1824, 0, -672, 0, -448, -1988, -558, 0, 0, 0, 392, -2352, -1120, 0, 168, 0, 1456, 0, 0, -2576, 128, 3420, -392, 0, 1680, 0, -2828, 224, 0, 2158, -504, 0, -2688, 0, -16, 3328, -1664, 4648, 0, 0, 1008, 0, 924, 0, -560, 2124, 4256, 0, 0, 0, -144, -1680, -16, 0, 588, 0, 2576, 0, 0, 1488, -784, -28, 672, 0, 3360, 0, -928, -336, 0, 2432, -1510, 0, 840, 0, -2884, 3920, -896, -1206, 0, 0, -4648, 0, -1680, 0, -2016, 5656, 532, 0, 0, 0, 2240, 1008, -6080, 0, 6272, 0, 4032, 0, 0, 7808, 4480, -6660, -1988, 0, 3348, 0, -84, -3472, 0, -1848, -3976, 0, 784, 0, -2352, -304, -6720, -1176, 0, 0, 336, 0, -1428, 0, -2912, 3584, 10024, 0, 0, 0, -2576, -3136, 2816, 0, 3420, 0, 2352, 0, 0, -1344, -3360, 1676, -280, 0, -5656, 0, 224, 12576, 0, -5852, 2158, 0, -1008, 0, -1960, -3920, -8960, 5768, 0, 0, 96, 0, 3328, 0, -7936, -5124, 4648, 0, 0, 0, 3556, 11792, 3360, 0, 1568, 0, 1848, 0, 0, -3360, 224, -4480, 2124, 0, 8512, 0, -14252, -448, 0, -5484, -9408, 0, 864, 0, -1680, -1120, -352, -9434, 0, 0, -3528, 0, -7812, 0, -5152, -4368, -4200, 0, 0, 0, 1488, 7952, -4704, 0, -28, 0, 1344, 0, 0, -5488, 11200, -4564, 952, 0, 5568, 0, -336, -5040, 0, 2856, 2432, 0, 9060, 0, -9380, -20048, 2800, -5376, 0, 0, -5768, 0, 3920, 0, -5376, -12260, -1206, 0, 0, 0, -196, -9952, 9296, 0, 10584, 0, 10080, 0, 0, -14560, -1344, 20412, 5656, 0, -3192, 0, -17276, -6352, 0, 10974, 12376, 0, 4480, 0, 1008, 23520, 2432, 140, 0, 0, 12544, 0, 1176, 0, 13440, -16800, 5824, 0, 0, 0, 7808, -5376, 12544, 0, -6660, 0, 11928, 0, 0, 4256, 11160, -7112, -6328, 0, -168, 0, -3472, -3136, 0, 24804, -1848, 0, -7952, 0, 6720, -7728, -1568, -24556, 0, 0, 14112, 0, -304, 0, -4480, 28504, -1176, 0, 0, 0, 15428, 672, -672, 0, -2016, 0, -2856, 0, 0, 15264, -17472, -7588, 3584, 0, 20048, 0, 8232, -3696, 0, 558, 3920, 0, 15456, 0, -3136, 8400, 4608, -7164, 0, 0, -20520, 0, -6692, 0, 7840, -5428, -27272, 0, 0, 0, -1344, -4448, -20160, 0, 1676, 0, -560, 0, 0, -1904, 11312, 13944, -12992, 0, -1344, 0, 12576, 35392, 0, -25760, -5852, 0, -12948, 0, -1484, -2608, 2016, 18760, 0, 0, -3920, 0, -3920, 0, 3584, -1152, 5768, 0, 0, 0, -28812, 38640, 320, 0, 12768, 0, -19968, 0, 0, 4704, -2560, -10192, -5124, 0, -27888, 0, 10304, -21168, 0, -5964, -840, 0, 7112, 0, 11792, 6272, -1344, 21874, 0, 0, 3136, 0, 7448, 0, -3696, 34552, 28392, 0, 0, 0, -3360, -24752, 4928, 0, -4480, 0, -12744, 0, 0, -11760, -17024, -7424, -8344, 0, -28504, 0, -448, 46480, 0, -2352, -5484, 0, -18816, 0, 15820, -12080, 2880, 31188, 0, 0, 10080, 0, -1120, 0, -576, -13188, -9434, 0, 0, 0, -27832, -1008, -11760, 0, -48888, 0, -15624, 0, 0, 12656, -30912, -28644, -4368, 0, -8400, 0, 42560, -32176, 0, -42476, -18592, 0, -8928, 0, 7952, 27328, -3136, -13440, 0, 0, 168, 0, 13692, 0, -2688, 7564, -32928, 0, 0, 0, -5488, 4256, -4480, 0, -4564, 0, 1904, 0, 0, 4112, 18560, -30856, 50680, 0, 2016, 0, -5040, 144, 0, 23684, 2856, 0, -14592, 0, 2744, -38640, 30200, 16968, 0, 0, -18760, 0, -20048, 0, -1120, -588, -5376, 0, 0, 0, 22484, -7840, 11536, 0, -1288, 0, -23520, 0, 0, 3024, -3584, 20156, -12260, 0, 7236, 0, 47880, -15904, 0, 13384, 18816, 0, -392, 0, -9952, 54544, 55776, -3360, 0, 0, 21168, 0, 13132, 0, 33600, -1960, 1736, 0, 0, 0, -14560, -18032, 13440, 0, 20412, 0, -33936, 0, 0, 928, -10640, 68096, 3136, 0, -34552, 0, -6352, -18592, 0, -18816, 10974, 0, 24752, 0, 30212, -43344, -8960, -37802, 0, 0, -6048, 0, 23520, 0, 53504, -5544, 140, 0, 0, 0, 1344, -34864, -25088, 0, -58072, 0, 2352, 0, 0, -23264, -5376, 57624, -16800, 0, 11648, 0, -16268, -25536, 0, 78932, 46592, 0, -46848, 0, -5376, 56560, -10752, 70532, 0, 0, 39960, 0, 2324, 0, 39760, -20608, -55496, 0, 0, 0, 4256, -43680, -4464, 0, -7112, 0, -12656, 0, 0, 27360, 336, 10080, -30184, 0, 20832, 0, -3136, -9408, 0, -532, 24804, 0, 11088, 0, 62720, -56784, 15904, -48780, 0, 0, 13440, 0, -7728, 0, -9408, 32536, -24556, 0, 0, 0, 29736, 43376, 47040, 0, -22624, 0, 1824, 0, 0, 16688, 44800, -7812, 28504, 0, 7056, 0, 43428, -37520, 0, -1622, 7672, 0, 30856, 0, 672, 17264, -4032, -31640, 0, 0, -4032, 0, -4032, 0, 5712, -17556, -23520, 0, 0, 0, 15264, 18624, -11648, 0, -7588, 0, -21504, 0, 0, -18480, -40096, 1988, 29792, 0, 16464, 0, -3696, 97776, 0, -62300, 558, 0, 7840, 0, -65268, -74256, 51520, 26624, 0, 0, 18816, 0, 8400, 0, -13312, -85120, -7164, 0, 0, 0, -5880, 37184, -68400, 0, 20832, 0, -13384, 0, 0, -21024, -3136, 17304, -5428, 0, -54544, 0, 10192, -92208, 0, -27384, -44184, 0, 8064, 0, -4448, 2352, -13440, -11452, 0, 0, -10056, 0, 54460, 0, 1120, -2548, 7392, 0, 0, 0, -1904, -21280, 67872, 0, 13944, 0, -25984, 0, 0, -101360, -4480, -76500, -168, 0, -75456, 0, 35392, 16992, 0, 40770, -25760, 0, 35112, 0, 34048, -9328, -43160, -5488, 0, 0, -2968, 0, -2608, 0, 12096, 9628, 18760, 0, 0, 0, -88172, 24752, 7840, 0, 11760, 0, 23520, 0, 0, 90688, 78848, -44968, -1152, 0, -34608, 0, -16380, -66976, 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, 8, 2, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "8.4.b.a", "char_is_minimal": true, "conrey_index": 101, "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], [1, 1], [0, -2], [-6, 2], [0, 0], [14, -2], [8, 0], [-20, -4], [-1, 0], [0, 0], [0, -6], [28, 12], [0, -20], [8, 8], [0, 0], [8, -24], [14, 0], [-1, -1], [0, -14], [0, 0], [0, -16], [42, -6], [152, 0], [-56, 40], [0, 0], [140, -20], [0, -52], [-48, 16], [0, -60], [0, 0], [224, 0], [176, -16], [-84, 0], [14, 14], [0, 0], [6, -2], [0, -92], [98, -14], [-280, 0], [0, 0], [-70, 0], [112, -16], [0, 166], [84, 36], [0, 0], [152, 152], [-336, 0], [-336, -16], [-279, 0], [0, 0], [0, -28], [280, 120], [0, -12], [364, -52], [0, 0], [-160, -32], [-196, 0], [420, -60], [0, 202], [0, 0], [0, 36], [224, 224], [-8, 0], [288, 160], [0, 0], [-84, -84], [0, -66], [-84, 28], [0, -304], [0, 0], [-72, 0], [20, 4], [294, 0], [644, -92], [0, 0], [196, 84], [0, -48], [-280, -280], [-464, 0], [0, 0], [-755, 0], [-70, -70], [0, 206], [224, 96], [0, 0], [-1162, 166], [-840, 0], [-168, 120], [266, 0], [0, 0], [0, -160], [-912, 304], [0, -448], [-336, -336], [0, 0], [-224, -352], [-994, 0], [-279, -279], [0, 6], [0, 0]]}