# Stored data for newform 208.4.a.g, downloaded from the LMFDB on 25 April 2024. {"label": "208.4.a.g", "space_label": "208.4.a", "level": 208, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021597831332048, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1134508627831255991, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-7, 1]]], "qexp_display": "q+7q^{3}-7q^{5}+13q^{7}+22q^{9}+26q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3328, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 12.272397281194047, "hecke_ring_index": 1, "level_radical": 26, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [208, 1, [79, 53, 145], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "0.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.954", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.909", "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], [13, -1]], "trace_display": [0, 7, -7, 13], "traces": [0, 1, 0, 7, 0, -7, 0, 13, 0, 22, 0, 26, 0, 13, 0, -49, 0, 77, 0, 126, 0, 91, 0, 96, 0, -76, 0, -35, 0, -82, 0, -196, 0, 182, 0, -91, 0, -131, 0, 91, 0, 336, 0, 201, 0, -154, 0, 105, 0, -174, 0, 539, 0, -432, 0, -182, 0, 882, 0, 294, 0, -56, 0, 286, 0, -91, 0, -478, 0, 672, 0, -9, 0, 98, 0, -532, 0, 338, 0, -1304, 0, -839, 0, 308, 0, -539, 0, -574, 0, -1190, 0, 169, 0, -1372, 0, -882, 0, 70, 0, 572, 0, 420, 0, -588, 0, -637, 0, 684, 0, 373, 0, -917, 0, -1734, 0, -672, 0, 286, 0, 1001, 0, -655, 0, 2352, 0, 1407, 0, -1892, 0, 1407, 0, -1435, 0, 1638, 0, 245, 0, -1776, 0, 1869, 0, 735, 0, 338, 0, 574, 0, -1218, 0, 2466, 0, 3323, 0, 1694, 0, 1372, 0, -2730, 0, -3024, 0, 1248, 0, 544, 0, -1274, 0, -1624, 0, 169, 0, 2772, 0, -336, 0, -988, 0, 2058, 0, 3029, 0, -28, 0, -392, 0, 917, 0, 2002, 0, -455, 0, -422, 0, 492, 0, -637, 0, 2991, 0, 70, 0, -3346, 0, -1066, 0, -2352, 0, 2112, 0, 3276, 0, -2851, 0, -63, 0, -1407, 0, -2548, 0, 686, 0, 1001, 0, -217, 0, -1672, 0, 2576, 0, 455, 0, 2366, 0, 3061, 0, -735, 0, -9128, 0, 3477, 0, -1610, 0, -4928, 0, 1218, 0, 1638, 0, 2156, 0, -1008, 0, 2496, 0, -3773, 0, 6041, 0, -1703, 0, -1804, 0, 3708, 0, 3024, 0, -8330, 0, 8344, 0, 1617, 0, 1183, 0, -1976, 0, -3820, 0, -4312, 0, -6214, 0, 5292, 0, -6174, 0, 4368, 0, 1016, 0, 490, 0, -903, 0, -2058, 0, -910, 0, 1248, 0, 2613, 0, 2940, 0, 392, 0, -2114, 0, -4116, 0, -3402, 0, -10689, 0, -2002, 0, -7054, 0, -2132, 0, 4788, 0, 9702, 0, -988, 0, 2611, 0, 1365, 0, -9704, 0, -2882, 0, 3346, 0, -10449, 0, -12138, 0, -5096, 0, -6721, 0, -4704, 0, 621, 0, 12481, 0, -455, 0, -1400, 0, 63, 0, 7007, 0, 4968, 0, 9017, 0, -4585, 0, -686, 0, -8722, 0, 7392, 0, -5616, 0, 10012, 0, 9849, 0, -1066, 0, 3372, 0, -13244, 0, 847, 0, -2366, 0, 4422, 0, 11314, 0, 7392, 0, -10045, 0, 9128, 0, 1862, 0, 11466, 0, 6820, 0, -2548, 0, 5873, 0, -3406, 0, -12992, 0, -12432, 0, 3822, 0, -2156, 0, 13083, 0, 7343, 0, -5059, 0, 2310, 0, -5852, 0, -728, 0, 2366, 0, -3243, 0, 11599, 0, 4018, 0, 12096, 0, 17374, 0, -3828, 0, -989, 0, 8330, 0, 17262, 0, -14474, 0, 8736, 0, 23261, 0, -1183, 0, -1594, 0, -2695, 0, -5915, 0, 11072, 0, 9604, 0, -1260, 0, -6214, 0, -19110, 0, 5226, 0, -9576, 0, -9504, 0, 12033, 0, -1703, 0, 8736, 0, -490, 0, 2280, 0, 3808, 0, -16767, 0, -6314, 0, -4004, 0, -117, 0, -12840, 0, -11368, 0, 2198, 0, -2940, 0, 1183, 0, -17066, 0, 1274, 0, -4410, 0, 4116, 0, 2730, 0, -2352, 0, 2583, 0, -18620, 0, -6916, 0, -15092, 0, -2951, 0, 6468, 0, 4368, 0, -4788, 0, 21203, 0, -4524, 0, -16833, 0, -196, 0, -2611, 0, 8615, 0, -1232, 0, -10332, 0, -16952, 0, 6419, 0, 8535, 0, 2613, 0, 14014, 0, 4641, 0, 12138, 0, -10907, 0, -4793, 0, 5563, 0, -2954, 0, -7296, 0, 24038, 0, 3444, 0, 4004, 0, -11232, 0, -2002, 0, 21224, 0, -24696, 0, 20937, 0, 4354, 0, -7007, 0, 490, 0, -7310, 0, -7595, 0, -10516, 0, 4585, 0, 826, 0, -7462, 0, 1365, 0, 14590, 0, -16464, 0, 4888, 0, 11004, 0, -3360, 0, -15470, 0, -349, 0, 22932, 0, -10087, 0, 4975, 0, -19957, 0, 13244, 0, -2262, 0, -198, 0, 3950, 0, 3682, 0, -9849, 0, -10402, 0, 7644, 0, -17836, 0, -31680, 0, 10045, 0, 2156, 0, -21940, 0, -31374, 0, 7007, 0, -11466, 0, -7872, 0, -1519, 0, -1456, 0, 18013, 0, 2660, 0, -10640, 0, 910, 0, 18032, 0, 9336, 0, 12432, 0, 3185, 0, -5616, 0, -4200, 0, 7436, 0, -13083, 0, 25872, 0, 21427, 0, 9872, 0, -16506, 0, -5145, 0, 5460, 0, 28450, 0, -28688, 0, -18816, 0, -2366, 0, 24339, 0, -32718, 0, -7644, 0, -11270, 0, 6232, 0, 22834, 0, -11843, 0, 15477, 0, 7875, 0, 8526, 0, -12428, 0, 2140, 0, 11466, 0, -31971, 0, -17262, 0, 6776, 0, 8892, 0, 7432, 0, -7056, 0, -23261, 0, 20176, 0, 17472, 0, -9478, 0, 4849, 0, -11858, 0, 3822, 0, -12096, 0, 42287, 0, 17941, 0, 14896, 0, -11921, 0, 42336, 0, -234, 0, 2870, 0, 19110, 0, -6664, 0, 25956, 0, -22542, 0, -728, 0, 21168, 0, -1442, 0, 8085, 0, -26180, 0, 2548, 0, -8736, 0, 58408, 0, 30207, 0, -21140, 0, 11319, 0, -3808, 0, 25326, 0, 3718, 0, 569, 0, 8538, 0, -13832, 0, 32702, 0, -21154, 0, -26740, 0, -13398, 0, 11368, 0, 6860, 0, 2184, 0, -17665, 0, -43498, 0, -1183, 0, -8515, 0, 37044, 0, -12576, 0, 36687, 0, -19404, 0, 36806, 0, -4900, 0, 30576, 0, 13697, 0, 2352, 0, 7112, 0, -33904, 0, -6214, 0, 1540, 0, 18291, 0, 6239, 0, -6321, 0, 133, 0, 26003, 0, -14406, 0, 31248, 0, -24596, 0, -21814, 0, 13230, 0, -21203, 0, 8736, 0, 16072, 0, -33264, 0, 18291, 0, 196, 0, 38253, 0, 9240, 0, -36374, 0, 8008, 0, 2744, 0, -18655, 0, 27648, 0, -14798, 0, -117, 0, 9956, 0, -12936, 0, 756, 0, -21924, 0, -23814, 0, -14014, 0, 20846, 0, -74823, 0, -41321, 0, 32256, 0, 3185, 0, -54966, 0, 1274, 0, -49378, 0, -44553, 0, 2954, 0, -14924, 0, -23088, 0, 8625, 0, 15048, 0, -3444, 0, 27907, 0, 67914, 0, 16443, 0, 24297, 0, -6916, 0, -45414, 0, -30940, 0, 8206, 0, 8981, 0, -20937, 0, 9555, 0, 19296, 0, 17414, 0, -67928, 0, -490, 0, -23702, 0, 4585, 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": "13.4.a.a", "char_is_minimal": false, "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], [7], [0], [-7], [0], [13], [0], [22], [0], [26], [0], [13], [0], [-49], [0], [77], [0], [126], [0], [91], [0], [96], [0], [-76], [0], [-35], [0], [-82], [0], [-196], [0], [182], [0], [-91], [0], [-131], [0], [91], [0], [336], [0], [201], [0], [-154], [0], [105], [0], [-174], [0], [539], [0], [-432], [0], [-182], [0], [882], [0], [294], [0], [-56], [0], [286], [0], [-91], [0], [-478], [0], [672], [0], [-9], [0], [98], [0], [-532], [0], [338], [0], [-1304], [0], [-839], [0], [308], [0], [-539], [0], [-574], [0], [-1190], [0], [169], [0], [-1372], [0], [-882], [0], [70], [0], [572], [0]]}