# Stored data for newform 117.4.g.f, downloaded from the LMFDB on 25 April 2024. {"label": "117.4.g.f", "space_label": "117.4.g", "level": 117, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22518410520821877, "dim": 16, "is_polredabs": true, "trace_hash": 2304617553794452125, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [24920064, 0, 21016320, 0, 13705540, 0, 2869882, 0, 424113, 0, 33440, 0, 1899, 0, 52, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-5-5\\beta _{2}+\\beta _{3}+\\beta _{6})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "g", "char_is_real": false, "Nk2": 1872, "analytic_conductor": 6.9032234706716515, "hecke_ring_index": 48, "level_radical": 39, "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": [117, 3, [92, 28], [3, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [3, 13], "conrey_indexes": [55, 100], "field_disc": 58617471833500478829542608399355655750494453760000, "field_disc_factorization": [[2, 22], [3, 8], [5, 4], [13, 6], [29, 4], [199, 4], [5023, 4]], "field_poly": [24920064, 0, 21016320, 0, 13705540, 0, 2869882, 0, 424113, 0, 33440, 0, 1899, 0, 52, 0, 1], "hecke_ring_index_factorization": [[2, 4], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.466", "prec": 20}, {"__RealLiteral__": 0, "data": "3.158", "prec": 17}, {"__RealLiteral__": 0, "data": "1298.490", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "223194.517", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 0, 0, 22], "traces": [0, 16, 0, 0, -40, 0, 0, 22, 0, 0, -36, 0, 0, 36, 0, 0, -204, 0, 0, -244, 0, 0, -136, 0, 0, 708, 0, 0, 452, 0, 0, 484, 0, 0, -2584, 0, 0, -1018, 0, 0, 3400, 0, 0, -74, 0, 0, 896, 0, 0, -298, 0, 0, -1676, 0, 0, -1300, 0, 0, -812, 0, 0, -1148, 0, 0, 7272, 0, 0, 2198, 0, 0, 4400, 0, 0, -4352, 0, 0, -6936, 0, 0, 3724, 0, 0, -5436, 0, 0, 890, 0, 0, -3528, 0, 0, -4754, 0, 0, 3104, 0, 0, 4370, 0, 0, -4180, 0, 0, 6900, 0, 0, 5596, 0, 0, 9708, 0, 0, -5904, 0, 0, -6132, 0, 0, 1152, 0, 0, -8792, 0, 0, -4772, 0, 0, -710, 0, 0, -25436, 0, 0, 6048, 0, 0, 20716, 0, 0, -5210, 0, 0, 28928, 0, 0, -2, 0, 0, 26888, 0, 0, -8616, 0, 0, -18104, 0, 0, -9672, 0, 0, -27844, 0, 0, -3726, 0, 0, -5064, 0, 0, -10688, 0, 0, 18972, 0, 0, 19206, 0, 0, 2688, 0, 0, 22412, 0, 0, 13776, 0, 0, 26280, 0, 0, -4960, 0, 0, -10168, 0, 0, -14200, 0, 0, -23790, 0, 0, 2724, 0, 0, -9134, 0, 0, -60228, 0, 0, 498, 0, 0, 26584, 0, 0, -15518, 0, 0, 65792, 0, 0, 18472, 0, 0, 17704, 0, 0, -18048, 0, 0, -49164, 0, 0, 27896, 0, 0, -35952, 0, 0, -12450, 0, 0, -3584, 0, 0, -18040, 0, 0, 28828, 0, 0, 16096, 0, 0, -16068, 0, 0, 26560, 0, 0, 7280, 0, 0, 48876, 0, 0, -67096, 0, 0, -10946, 0, 0, 32552, 0, 0, -11574, 0, 0, 16056, 0, 0, -14026, 0, 0, -33552, 0, 0, -19546, 0, 0, 7424, 0, 0, -8072, 0, 0, 67256, 0, 0, 12182, 0, 0, 53936, 0, 0, -41820, 0, 0, -65728, 0, 0, 17540, 0, 0, -24476, 0, 0, -9348, 0, 0, -12632, 0, 0, -21918, 0, 0, -6764, 0, 0, 4702, 0, 0, -15856, 0, 0, 30400, 0, 0, 53372, 0, 0, 63188, 0, 0, 23984, 0, 0, -11506, 0, 0, 70928, 0, 0, -17196, 0, 0, 27416, 0, 0, -7592, 0, 0, -15584, 0, 0, -21054, 0, 0, -18116, 0, 0, -35812, 0, 0, 35840, 0, 0, -32198, 0, 0, -121408, 0, 0, -72864, 0, 0, -10580, 0, 0, 42344, 0, 0, 17488, 0, 0, -370, 0, 0, -880, 0, 0, 69290, 0, 0, 42248, 0, 0, -960, 0, 0, 57716, 0, 0, -35448, 0, 0, 3112, 0, 0, 80888, 0, 0, 16488, 0, 0, 45490, 0, 0, -125536, 0, 0, 11440, 0, 0, -2508, 0, 0, -18122, 0, 0, -85084, 0, 0, -37040, 0, 0, -20272, 0, 0, -26276, 0, 0, 9392, 0, 0, 20160, 0, 0, -93904, 0, 0, 38572, 0, 0, 1248, 0, 0, 33076, 0, 0, 26992, 0, 0, -58408, 0, 0, 116432, 0, 0, 58402, 0, 0, 33216, 0, 0, 36668, 0, 0, 83236, 0, 0, -184452, 0, 0, -113768, 0, 0, 18032, 0, 0, 139008, 0, 0, 107482, 0, 0, -139304, 0, 0, 15798, 0, 0, 47132, 0, 0, -30912, 0, 0, 135068, 0, 0, -46516, 0, 0, -66912, 0, 0, 4632, 0, 0, -137616, 0, 0, -24956, 0, 0, -238928, 0, 0, 5272, 0, 0, 115148, 0, 0, -85860, 0, 0, 117248, 0, 0, 12310, 0, 0, -12292, 0, 0, 68934, 0, 0, 79596, 0, 0, -6218, 0, 0, 17808, 0, 0, -70584, 0, 0, -21472, 0, 0, 72380, 0, 0, 316936, 0, 0, 88388, 0, 0, -17528, 0, 0, 25200, 0, 0, -45932, 0, 0, 35076, 0, 0, 65344, 0, 0, -87430, 0, 0, -47552, 0, 0, -35776, 0, 0, -167560, 0, 0, -54468, 0, 0, -290512, 0, 0, -15548, 0, 0, 58304, 0, 0, -58544, 0, 0, 163128, 0, 0, -99686, 0, 0, 13508, 0, 0, 210514, 0, 0, -6212, 0, 0, -55774, 0, 0, 206056, 0, 0, -212288, 0, 0, -38972, 0, 0, 77168, 0, 0, 100400, 0, 0, 132788, 0, 0, -94160, 0, 0, 107660, 0, 0, 158848, 0, 0, 43536, 0, 0, 55580, 0, 0, -134950, 0, 0, -183664, 0, 0, -91730, 0, 0, -316768, 0, 0, -61742, 0, 0, -398352, 0, 0, 276, 0, 0, 67612, 0, 0, 185400, 0, 0, 76388, 0, 0, -34284, 0, 0, 140720, 0, 0, 224084, 0, 0, 89184, 0, 0, -5002, 0, 0, 45964, 0, 0, -2380, 0, 0, -128188, 0, 0, 185848, 0, 0, 59808, 0, 0, 137432, 0, 0, -61936, 0, 0, 81254, 0, 0, 110328, 0, 0, -103332, 0, 0, 10176, 0, 0, -127488, 0, 0, -276912, 0, 0, -56918, 0, 0, 60352, 0, 0, 48320, 0, 0, -280400, 0, 0, -248324, 0, 0, -81660, 0, 0, 56896, 0, 0, 237060, 0, 0, -80990, 0, 0, 23328, 0, 0, 39362, 0, 0, -101124, 0, 0, -21436, 0, 0, 208460, 0, 0, -214208, 0, 0, 85204, 0, 0, -8956, 0, 0, 338176, 0, 0, 108720, 0, 0, 151416, 0, 0, -43656, 0, 0, 64736, 0, 0, 64876, 0, 0, 268996, 0, 0, -184592, 0, 0, -152592, 0, 0, -83618, 0, 0, 44728, 0, 0, -84594, 0, 0, -476528, 0, 0, -17528, 0, 0, 63592, 0, 0, 169380, 0, 0, 85840, 0, 0, -8608, 0, 0, -18908, 0, 0, 230920, 0, 0, 181640, 0, 0, 10382, 0, 0, 34144, 0, 0, -236508, 0, 0, 63856, 0, 0, 222148, 0, 0, -331936, 0, 0, 108372, 0, 0, -156256, 0, 0, 58054, 0, 0, 124492, 0, 0, -165512, 0, 0, -309216, 0, 0, -103680, 0, 0, -10344, 0, 0, -52472, 0, 0, 220072, 0, 0, 23824, 0, 0, 343768, 0, 0, 32712, 0, 0, -149720, 0, 0, -3124, 0, 0, -106360, 0, 0, -33268, 0, 0, 230424, 0, 0, 131644, 0, 0, 47968, 0, 0, 181920, 0, 0, 40576, 0, 0, 15796, 0, 0, -239652, 0, 0, 86472, 0, 0, 366848, 0, 0, 8274, 0, 0, -140840, 0, 0, -142496, 0, 0, -147480, 0, 0, -53712, 0, 0, -321344, 0, 0, -60868, 0, 0, -37256, 0, 0, -138180, 0, 0, -133592], "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, 13, 3, 1, 3, 0], [1, 1, 39, 9, -1, 6, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "117.4.g.f", "char_is_minimal": true, "conrey_index": 55, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -5, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, -5, 0, 0, 0, 1, 0, -1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 1, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, -2, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 7, 0, 0, 0, 2, 0, 1, 2, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 25, 0, 0, 0, -9, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-31, 0, -31, 6, 1, 0, 6, 1, -1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, -6, -3, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15, 0, -15, 8, -7, 0, 8, -7, 1, 0, -1, 0, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, 0, 0, 0, -5, 0, -2, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [46, 0, 0, 0, 0, 0, 0, -6, 1, 0, 0, 0, 0, 0, 0, 0], [0, 10, 0, 0, 0, -6, 0, 0, 0, -11, 0, 3, -7, -2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -57, 0, 1, 0, 6, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 10, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [28, 0, 0, -8, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, -19, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-163, 0, 0, 27, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 17, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 126, 0, 7, 0, -12, 0, 0, 0, -2, 0, 0, 0, 0, 0], [0, -89, 0, 0, 0, -89, 0, 0, 0, -5, 0, -6, -5, 6, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [212, 0, 0, -43, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 49, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, -11, -26, 7, 0, -26, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, -37, 0, 0, 0, -37, 0, 0, 0, 23, 0, -2, 23, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [113, 0, 113, -18, -1, 0, -18, -1, 3, 0, -3, 0, 0, 0, 0, 0], [0, 33, 0, 0, 0, 33, 0, 0, 0, 11, 0, -2, 11, 2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 37, 0, 8, 0, 10, 0, 0, 0, -7, 0, 0, 0, 0, 0], [0, 76, 0, 0, 0, 0, 0, 0, 0, 21, 0, 5, 0, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-186, 0, -162, 25, -8, 0, 54, -1, 5, 0, -6, 0, 0, 0, 0, 0], [0, 60, 0, 0, 0, 60, 0, 0, 0, 19, 0, -2, 19, 2, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 167, 0, -7, 0, -24, 0, 0, 0, -11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -59, 0, 0, 0, 0, 0, 0, 11, -2, 0, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-102, 0, -102, 61, 7, 0, 61, 7, 5, 0, -5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -6, 4, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-148, 0, -148, -10, 15, 0, -10, 15, -3, 0, 3, 0, 0, 0, 0, 0], [0, 50, 0, 0, 0, 0, 0, 0, 0, -47, 0, 5, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [449, 0, 0, -57, 0, 0, 0, 16, -6, 0, 0, 0, 0, 0, 0, 0], [0, -63, 0, 0, 0, -156, 0, 0, 0, -8, 0, -6, -12, 2, -1, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -273, 0, 1, 0, 30, 0, 0, 0, -8, 0, 0, 0, 0, 0], [0, -295, 0, 0, 0, 0, 0, 0, 0, 29, 0, -21, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [285, 0, 0, 28, 0, 0, 0, -23, 17, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, -11, 14, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-273, 0, 0, -6, 0, 0, 0, -8, -12, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 206, 0, 0, 0, 0, 0, 0, -8, -3, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 867, 0, -9, 0, -76, 0, 0, 0, 9, 0, 0, 0, 0, 0], [0, -176, 0, 0, 0, -176, 0, 0, 0, -28, 0, 26, -28, -26, -6, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [234, 0, 0, -16, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 402, 0, 0, 0, 0, 0, 0, 0, -6, 0, 19, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-675, 0, -675, 35, -16, 0, 35, -16, 2, 0, -2, 0, 0, 0, 0, 0], [0, -51, 0, 0, 0, -51, 0, 0, 0, -13, 0, 8, -13, -8, -7, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [102, 0, 102, -74, 19, 0, -74, 19, -18, 0, 18, 0, 0, 0, 0, 0], [0, 169, 0, 0, 0, 169, 0, 0, 0, -40, 0, 19, -40, -19, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 447, 0, -41, 0, -56, 0, 0, 0, 17, 0, 0, 0, 0, 0], [0, -44, 0, 0, 0, 0, 0, 0, 0, -32, 0, -24, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-275, 0, 32, -22, 34, 0, -12, -7, -5, 0, 11, 0, 0, 0, 0, 0], [0, 191, 0, 0, 0, 191, 0, 0, 0, -29, 0, 0, -29, 0, -9, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -395, 0, 15, 0, -22, 0, 0, 0, 13, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -39, 0, 0, 0, 0, 0, 0, -65, -22, 0, 15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [558, 0, 558, 58, -48, 0, 58, -48, -1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -33, 0, 0, 0, 0, 0, 0, 57, 25, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-528, 0, -528, 34, 14, 0, 34, 14, -8, 0, 8, 0, 0, 0, 0, 0]]}