# Stored data for newform 200.4.a.g, downloaded from the LMFDB on 28 March 2024. {"label": "200.4.a.g", "space_label": "200.4.a", "level": 200, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021597831332040, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 306303680102536196, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-4, 1]]], "qexp_display": "q+4q^{3}-24q^{7}-11q^{9}-44q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3200, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 11.800382001148122, "hecke_ring_index": 1, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [200, 1, [151, 101, 177], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5], "conrey_indexes": [1], "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": "0.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.209", "prec": 17}, {"__RealLiteral__": 0, "data": "4.809", "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], [5, 1]], "trace_display": [0, 4, 0, -24], "traces": [0, 1, 0, 4, 0, 0, 0, -24, 0, -11, 0, -44, 0, -22, 0, 0, 0, -50, 0, 44, 0, -96, 0, 56, 0, 0, 0, -152, 0, 198, 0, -160, 0, -176, 0, 0, 0, 162, 0, -88, 0, -198, 0, -52, 0, 0, 0, -528, 0, 233, 0, -200, 0, 242, 0, 0, 0, 176, 0, -668, 0, 550, 0, 264, 0, 0, 0, -188, 0, 224, 0, 728, 0, -154, 0, 0, 0, 1056, 0, -656, 0, -311, 0, -236, 0, 0, 0, 792, 0, 714, 0, 528, 0, -640, 0, 0, 0, 478, 0, 484, 0, 1566, 0, 968, 0, 0, 0, 780, 0, -1994, 0, 648, 0, 942, 0, 0, 0, 242, 0, 1200, 0, 605, 0, -792, 0, 0, 0, -1408, 0, -208, 0, -2692, 0, -1056, 0, 0, 0, -1626, 0, -684, 0, -2112, 0, 968, 0, 0, 0, 932, 0, 302, 0, 1352, 0, 550, 0, 0, 0, -3142, 0, 968, 0, -1344, 0, -3036, 0, 0, 0, 264, 0, -1713, 0, -484, 0, 2826, 0, 0, 0, -2672, 0, 3084, 0, -2418, 0, 2200, 0, 0, 0, 2200, 0, 3648, 0, -960, 0, -2882, 0, 0, 0, -1086, 0, 88, 0, -752, 0, -4752, 0, 0, 0, -616, 0, -1936, 0, -3476, 0, 2912, 0, 0, 0, 3840, 0, -616, 0, 1100, 0, -928, 0, 0, 0, -156, 0, -1634, 0, 4224, 0, 902, 0, 0, 0, -2624, 0, 1616, 0, 4818, 0, 2860, 0, 0, 0, -968, 0, -944, 0, -2140, 0, -2464, 0, 0, 0, -770, 0, -3888, 0, -2178, 0, 7400, 0, 0, 0, 2856, 0, -2794, 0, 8624, 0, 2112, 0, 0, 0, 1874, 0, 1760, 0, 3338, 0, -7172, 0, 0, 0, 4752, 0, -2413, 0, 1912, 0, -5214, 0, 0, 0, 6688, 0, -1232, 0, 1248, 0, 6264, 0, 0, 0, -396, 0, 3872, 0, -4056, 0, -2154, 0, 0, 0, 7386, 0, -8712, 0, 3120, 0, -2200, 0, 0, 0, -7976, 0, 12672, 0, -1132, 0, -1782, 0, 0, 0, 3342, 0, 3768, 0, 7040, 0, 2640, 0, 0, 0, -2244, 0, -6522, 0, 3344, 0, 11230, 0, 0, 0, 4800, 0, 1848, 0, -4923, 0, 2420, 0, 0, 0, -7120, 0, 2178, 0, -5808, 0, -6350, 0, 0, 0, -4356, 0, -7900, 0, -5632, 0, -10368, 0, 0, 0, 572, 0, 8830, 0, -2800, 0, -10768, 0, 0, 0, -9878, 0, -4224, 0, -13134, 0, 3520, 0, 0, 0, -7128, 0, 906, 0, -6504, 0, 16032, 0, 0, 0, -2736, 0, -5412, 0, -4642, 0, 5808, 0, 0, 0, -13200, 0, 3872, 0, 656, 0, -9490, 0, 0, 0, 2464, 0, 5544, 0, -2563, 0, -7652, 0, 0, 0, 1208, 0, -446, 0, 8712, 0, 5408, 0, 0, 0, -1562, 0, 7600, 0, 10582, 0, 10768, 0, 0, 0, 9876, 0, 4512, 0, -12568, 0, 2288, 0, 0, 0, -2662, 0, -352, 0, -3564, 0, -5376, 0, 0, 0, 15176, 0, -12144, 0, -8844, 0, -9900, 0, 0, 0, -17472, 0, 19404, 0, 1056, 0, -16488, 0, 0, 0, -6852, 0, -12954, 0, 3696, 0, -6688, 0, 0, 0, 23232, 0, 11304, 0, 10970, 0, 16940, 0, 0, 0, 8000, 0, -9031, 0, 7348, 0, 4356, 0, 0, 0, 12336, 0, -10252, 0, 198, 0, -9672, 0, 0, 0, 15268, 0, -6050, 0, 8712, 0, 15744, 0, 0, 0, -20854, 0, 1144, 0, 8800, 0, 19316, 0, 0, 0, 7464, 0, 7018, 0, 24420, 0, -3840, 0, 0, 0, -23234, 0, -11528, 0, 5664, 0, -10648, 0, 0, 0, 10604, 0, -7040, 0, -4344, 0, 13838, 0, 0, 0, 352, 0, -3960, 0, -5942, 0, 2068, 0, 0, 0, 3040, 0, -19008, 0, 11616, 0, 2530, 0, 0, 0, 19206, 0, 10996, 0, -8512, 0, -17136, 0, 0, 0, -7744, 0, -8100, 0, -6680, 0, -13904, 0, 0, 0, -5126, 0, -8008, 0, 6274, 0, -9084, 0, 0, 0, 23656, 0, 29392, 0, 15360, 0, 6762, 0, 0, 0, 1694, 0, 15276, 0, 11054, 0, 4400, 0, 0, 0, 11088, 0, -3712, 0, -24200, 0, 21278, 0, 0, 0, -8926, 0, -11472, 0, -624, 0, -8116, 0, 0, 0, -6536, 0, -5324, 0, -11764, 0, -11616, 0, 0, 0, 9900, 0, 3608, 0, -4698, 0, 7128, 0, 0, 0, -37584, 0, 24638, 0, 7216, 0, -8960, 0, 0, 0, 6464, 0, 16624, 0, -23232, 0, 19272, 0, 0, 0, -30216, 0, 19837, 0, 2600, 0, 3322, 0, 0, 0, 8272, 0, -14692, 0, -3872, 0, -28600, 0, 0, 0, 2596, 0, -18720, 0, -29616, 0, -8560, 0, 0, 0, -2894, 0, -9856, 0, 14762, 0, 47856, 0, 0, 0, 14696, 0, -7678, 0, -3080, 0, -27390, 0, 0, 0, -15552, 0, -8712, 0, -32032, 0, -30096, 0, 0, 0, -19756, 0, 29600, 0, -22608, 0, -12100, 0, 0, 0, -38854, 0, 26400, 0, -7854, 0, 6776, 0, 0, 0, -11176, 0, -14278, 0, -716, 0, 34496, 0, 0, 0, -2288, 0, -5808, 0, -23538, 0, 6616, 0, 0, 0, -27236, 0, 12070, 0, 7496, 0, -11650, 0, 0, 0, 24320, 0, -42024, 0, 14815, 0, 13352, 0, 0, 0, -14520, 0, -28688, 0, 9072, 0, -2414, 0, 0, 0, 37686, 0, 40644, 0, 19008, 0, 18656, 0, 0, 0, -9652, 0, 28864, 0, 4136, 0, -5258, 0, 0, 0, 13002, 0, -20856, 0, 49490, 0, -1100, 0, 0, 0, 14104, 0, 33792, 0, 13684, 0, -23232, 0, 0, 0, -4928, 0, -31680, 0, -12100, 0, 4992, 0, 0, 0, 12716, 0, -17226, 0, -39632, 0, 10384, 0, 0, 0, 64608, 0, 5704, 0, -1584, 0, -16016, 0, 0, 0, -10648, 0, 8162, 0, 10252, 0, -16224, 0, 0, 0, 55110, 0, -8616, 0, 16374, 0, -11088, 0, 0, 0, -8460, 0, 3388, 0, 29544, 0, 20502, 0, 0, 0, -34848, 0, 39024, 0, -4191, 0, -8580, 0, 0, 0, 36520, 0, -8800, 0, 20244, 0, 16416, 0, 0, 0, -50034, 0, -31416, 0, 21934, 0, -37128, 0, 0, 0, 50688, 0, -2912, 0, 27808, 0, -4528, 0, 0, 0, 28514, 0, -24624, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "8.4.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], [4], [0], [0], [0], [-24], [0], [-11], [0], [-44], [0], [-22], [0], [0], [0], [-50], [0], [44], [0], [-96], [0], [56], [0], [0], [0], [-152], [0], [198], [0], [-160], [0], [-176], [0], [0], [0], [162], [0], [-88], [0], [-198], [0], [-52], [0], [0], [0], [-528], [0], [233], [0], [-200], [0], [242], [0], [0], [0], [176], [0], [-668], [0], [550], [0], [264], [0], [0], [0], [-188], [0], [224], [0], [728], [0], [-154], [0], [0], [0], [1056], [0], [-656], [0], [-311], [0], [-236], [0], [0], [0], [792], [0], [714], [0], [528], [0], [-640], [0], [0], [0], [478], [0], [484], [0]]}