# Stored data for newform 105.3.t.a, downloaded from the LMFDB on 24 April 2024.
{"label": "105.3.t.a", "space_label": "105.3.t", "level": 105, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 1305720389737, "dim": 8, "is_polredabs": true, "nf_label": "8.0.3317760000.8", "trace_hash": 945510394774454898, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [81, 0, -126, 0, 187, 0, -14, 0, 1]]], "qexp_display": "q+(\\beta _{2}-\\beta _{4}-\\beta _{5})q^{2}+(-1+\\beta _{3}+\\beta _{5}+\\cdots)q^{3}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "t", "char_is_real": false, "Nk2": 945, "analytic_conductor": 2.8610427757831176, "hecke_ring_index": 1, "level_radical": 105, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [105, 6, [71, 22, 31], [3, 6, 4]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [3, 5, 7], "conrey_indexes": [11, 86], "field_disc": 3317760000, "field_disc_factorization": [[2, 16], [3, 4], [5, 4]], "field_poly": [81, 0, 36, 0, 7, 0, 4, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.038", "prec": 17}, {"__RealLiteral__": 0, "data": "7.232", "prec": 17}, {"__RealLiteral__": 0, "data": "5.940", "prec": 17}, {"__RealLiteral__": 0, "data": "390.683", "prec": 24}, {"__RealLiteral__": 0, "data": "986.271", "prec": 24}, {"__RealLiteral__": 0, "data": "39873.736", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, -4, 0, 56], "traces": [0, 8, 0, -4, 12, 0, 32, 56, 0, 8, -20, 0, 52, 8, 0, -40, -84, 0, -52, 36, 0, -28, -72, 0, 24, 20, 0, 56, 84, 0, -40, 24, 0, -72, -304, 0, -272, -12, 0, 96, 60, 0, 224, 48, 0, 20, -148, 0, 328, 392, 0, -164, -388, 0, -160, 120, 0, -352, -200, 0, -20, 264, 0, 56, -88, 0, 36, 288, 0, 88, -140, 0, 348, -288, 0, 20, 1336, 0, -168, -344, 0, -28, -180, 0, 364, 320, 0, 140, 36, 0, 80, 56, 0, 164, -52, 0, -320, -448, 0, -72, -60, 0, 292, -128, 0, -280, 1144, 0, -116, -184, 0, -496, -588, 0, 284, 20, 0, 408, -848, 0, -480, -232, 0, 180, -632, 0, -364, -968, 0, -124, 180, 0, 288, 252, 0, 20, -408, 0, -488, -256, 0, -728, -120, 0, -152, 160, 0, -196, 2008, 0, 80, -536, 0, 256, -504, 0, -648, -252, 0, 224, 680, 0, 1184, 152, 0, 0, 200, 0, 168, 656, 0, 488, 472, 0, 920, 140, 0, 272, 96, 0, -380, -864, 0, 32, 1212, 0, 236, 504, 0, 392, -920, 0, 164, -208, 0, -240, 588, 0, -72, 736, 0, 368, 848, 0, -184, 180, 0, 532, 716, 0, -280, 456, 0, 300, -1032, 0, -2640, 168, 0, -148, -60, 0, 212, -1792, 0, 80, 1680, 0, -1448, -264, 0, -504, -1680, 0, 948, 260, 0, 568, -2128, 0, 340, 1004, 0, 836, -656, 0, 720, -1364, 0, -680, 100, 0, -1904, -648, 0, -140, 908, 0, 392, -84, 0, 320, 644, 0, -324, -680, 0, 624, -1184, 0, -40, -376, 0, 672, -1504, 0, -1108, -872, 0, -1024, 420, 0, 208, 1552, 0, -40, -72, 0, 1000, 132, 0, 324, 304, 0, 1568, -80, 0, 360, 896, 0, 520, 336, 0, 88, 1876, 0, 256, 1472, 0, -1184, 400, 0, -1476, 232, 0, 140, -1584, 0, -1492, -360, 0, 1032, -1036, 0, -1196, 20, 0, 396, -1080, 0, 360, 764, 0, 1064, -340, 0, 2296, -288, 0, -1500, 400, 0, -3736, 2744, 0, 340, -1068, 0, -500, 1744, 0, 1056, 900, 0, 1544, 240, 0, -1148, 2712, 0, 600, -840, 0, 1184, -2716, 0, 776, -252, 0, 180, -920, 0, 2584, 1312, 0, -100, -1092, 0, -1120, 424, 0, -116, -56, 0, 1968, 840, 0, -352, -1072, 0, 660, 64, 0, -704, 180, 0, 612, -632, 0, -2464, -840, 0, 1232, -1376, 0, -1120, -1400, 0, -1788, 496, 0, -44, 4992, 0, 2128, -520, 0, -72, -324, 0, -140, -1584, 0, -572, 3108, 0, 120, 1848, 0, -972, -320, 0, -188, 48, 0, -520, -1768, 0, -1012, 1056, 0, 392, 2496, 0, -1664, -240, 0, -1496, -616, 0, 260, -540, 0, -1136, -64, 0, 4632, -232, 0, -20, -1340, 0, 252, -4072, 0, 20, 912, 0, 528, 2016, 0, -952, -4056, 0, -1316, 360, 0, -2536, 560, 0, -440, -2612, 0, 616, -4272, 0, -1024, 688, 0, 816, -980, 0, -180, -1240, 0, 360, -3248, 0, 160, 1096, 0, -140, -2100, 0, 2436, -400, 0, -128, 948, 0, 1240, -2016, 0, -448, 888, 0, 1012, 2808, 0, -3792, -1740, 0, -640, 592, 0, 140, -2096, 0, -792, -48, 0, 3632, 9352, 0, -24, 0, 0, -48, 6272, 0, 2920, -1576, 0, 932, 2680, 0, -1176, 3632, 0, -1648, -180, 0, -4704, -2408, 0, 320, 416, 0, 1712, -1952, 0, 72, -1740, 0, 1508, -1560, 0, -196, 720, 0, 1340, -1816, 0, 3176, -1260, 0, 392, -1272, 0, 1092, 1760, 0, -1992, -324, 0, -780, 2420, 0, 2548, 4352, 0, 360, 1828, 0, -504, 2240, 0, 136, 3252, 0, -120, 4256, 0, 512, 4008, 0, -1184, -812, 0, 980, -1520, 0, 2864, 212, 0, -360, 252, 0, 208, 956, 0, 2260, -4992, 0, -5472, -100, 0, -612, 3556, 0, 560, 2096, 0, 272, -3832, 0, 4624, 392, 0, -240, -900, 0, -3612, -6192, 0, -40, -3328, 0, 1968, -1512, 0, 1148, -3568, 0, -156, 20, 0, -2272, -364, 0, 360, 64, 0, -1164, -2640, 0, -4888, 800, 0, 1896, 1600, 0, -2240, -1472, 0, 140, 184, 0, -7080, -3136, 0, 136, -216, 0, -1784, 560, 0, 2408, -1304, 0, 400, 3464, 0, -504, -1184, 0, 2580, -1440, 0, 3408, -420, 0, 3540, -3532, 0, -260, -336, 0, -7808, 816, 0, 928, 576, 0, 2044, 1320, 0, 2200, -1104, 0, -2120, -896, 0, 1524, -3296, 0, -1288, -3048, 0, -4048, -1160, 0, -1472, -2588, 0, -1960, 1960, 0, -360, 3676, 0, 4248, 8008, 0, -2244, 200, 0, 760, -1296, 0, -400, -3416, 0, 1200, 2400, 0, -812, -1808, 0, -576, -3060, 0, -2672, -1288, 0, 400, 2212, 0, 1868, 5464, 0, 912, -4576, 0, -1312, -120, 0, -3472, 11472, 0, 1680, -1080, 0, -1720, -4116, 0, 2284, 3168, 0, -856, 3200, 0, 3024, 3064, 0, 920, 192, 0, 1988, 4576, 0, 336, -2556, 0, 8608, 140, 0, 3952, 2616, 0, 500, -7144, 0, 3072, 108, 0, -2644, 1616, 0, 2856, 1080, 0, 2212, 1312, 0, -720, -5936, 0, -3196, 1976, 0, -2312, 2312, 0, -624, 20, 0, -532, -2340, 0, -3360, 3768, 0, -780, -1316, 0, -2288, -1624, 0, 1072, -760, 0, 780, -1912, 0, 2600, 9288, 0, -864, 1336, 0, 1260, 2848, 0, -1040, 1620, 0, 376, -4424, 0, 740, -512, 0, -48, -12184, 0, -5528, 148, 0, -1640, -780, 0, -2548, 3888, 0, -1120, 5352, 0, 7656, -6776, 0, -1584, -6688, 0, 3436, -840, 0, 6288, 3060, 0, -680, -2488, 0, -868, 11520, 0, -2744, 3408, 0, -2192, 1260, 0, 5536, 2520, 0, -1600, -9104, 0, -728, -424, 0, -2436, 1120, 0, 2016, -120, 0, 3136, -2920, 0, -2440, 1764, 0, 1608, 5608, 0, -3852, -288, 0, 256, 1300, 0, -1708, 180, 0, 140, -432, 0, 4052, -1688, 0, -8288, -2856, 0, -2536, -1040, 0, -180, 8672, 0, 200, 1740, 0, 4128, -5092, 0, -3416, -2688, 0, 76, 1320, 0, 5416, -1792, 0, -480, 3304, 0, 48, -2304, 0, -5376, -3000, 0, 2160, 180, 0, -5096, -14264, 0, -180, 1064, 0, -1248, -840, 0, -2200, -6752, 0, -1384, 600], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "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": 20, "prim_orbit_index": 8, "minimal_twist": "105.3.t.a", "char_is_minimal": true, "conrey_index": 11, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, -1, 0, 0], [-1, 0, 0, 1, 0, 1, -1, 1], [3, 0, 0, -3, 0, -2, 0, -4], [0, 0, -1, 0, 0, 0, 0, 0], [4, -1, -2, 0, 3, -1, -2, -1], [7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, -9, 0, 3, 0], [0, 4, -1, 2, 6, 6, 0, 0], [-5, 0, 0, 5, 0, 1, 0, 2], [0, 0, 0, 0, 0, -3, 3, 0], [0, -7, 1, 13, -12, -12, 0, 0], [1, 10, 0, 0, 5, 10, 0, 10], [0, 0, 7, 0, -7, -7, 0, 0], [-5, -1, 1, 0, -3, -1, 1, -1], [0, 8, 0, -21, 4, 4, 0, 0], [0, 0, 0, 0, 0, -1, 8, 0], [-13, 0, 0, 13, 0, 13, 2, 10], [0, -14, 0, 9, -7, -7, 0, 0], [0, 0, -3, 0, 10, 0, -3, 0], [-7, 0, 0, 7, 0, 7, -7, 7], [-9, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 16, 16, 0, 0], [6, 0, 0, -6, 0, -24, -12, -15], [5, 0, 0, -5, 0, 0, 0, 0], [0, 0, -9, 0, 24, 24, 0, 0], [7, 5, 1, 0, -15, 5, 1, 5], [21, 0, 0, -21, 0, -14, 0, -28], [0, 0, 8, 0, -5, 0, 8, 0], [0, 7, -4, -10, 6, 6, 0, 0], [6, 0, 0, -6, 0, -7, 0, -14], [0, 0, 0, 0, 0, 5, 17, 0], [0, -9, 0, -18, -9, -9, 0, 0], [-38, 14, 0, 0, 7, 14, 0, 14], [0, 0, -7, 0, 0, 0, 0, 0], [-34, 4, -19, 0, 24, 4, -19, 4], [0, -26, 0, -3, -13, -13, 0, 0], [0, 0, 0, 0, 0, -44, -23, 0], [24, 0, 0, -24, 0, 21, -6, -9], [0, -18, 0, 15, -9, -9, 0, 0], [0, 0, 9, 0, 0, 0, 9, 0], [28, -7, -14, 0, 21, -7, -14, -7], [6, -10, 0, 0, -5, -10, 0, -10], [0, 0, 3, 0, 21, 21, 0, 0], [5, 0, 0, -5, 0, -14, 2, -8], [-37, 0, 0, 37, 0, 17, 0, 34], [0, 0, -13, 0, -26, -26, 0, 0], [41, -29, 17, 0, -24, -29, 17, -29], [49, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, -5, 0, 5, 0], [0, -10, 7, -41, -24, -24, 0, 0], [-97, 0, 0, 97, 0, 13, 0, 26], [0, 0, 0, 0, 0, -29, -17, 0], [0, 37, 2, -40, 24, 24, 0, 0], [15, 6, 0, 0, 3, 6, 0, 6], [0, 0, 21, 0, -63, 0, 21, 0], [-44, 23, -2, 0, 42, 23, -2, 23], [0, 26, 0, -50, 13, 13, 0, 0], [0, 0, 0, 0, 0, 58, -2, 0], [-5, 0, 0, 5, 0, 26, 13, 17], [0, 28, 0, 66, 14, 14, 0, 0], [0, 0, 20, 0, -41, 0, 20, 0], [0, 28, -7, 14, 42, 42, 0, 0], [-11, 12, 0, 0, 6, 12, 0, 12], [0, 0, -1, 0, -25, -25, 0, 0], [9, 0, 0, -9, 0, -9, 9, -9], [72, 0, 0, -72, 0, -4, 0, -8], [0, 0, -20, 0, 77, 77, 0, 0], [11, 31, 17, 0, -3, 31, 17, 31], [-35, 0, 0, 35, 0, 7, 0, 14], [0, 0, 12, 0, 15, 0, 12, 0], [0, -42, -30, 87, -9, -9, 0, 0], [-72, 0, 0, 72, 0, -7, 0, -14], [0, 0, 0, 0, 0, -62, -23, 0], [0, -5, 5, 5, 0, 0, 0, 0], [167, -78, 0, 0, -39, -78, 0, -78], [0, 0, 0, 0, 0, -21, 21, 0], [-21, 39, 33, 0, -27, 39, 33, 39], [0, -6, 0, -86, -3, -3, 0, 0], [0, 0, 0, 0, 0, -20, -21, 0], [-7, 0, 0, 7, 0, -20, -28, -32], [0, 18, 0, -45, 9, 9, 0, 0], [0, 0, -26, 0, -40, 0, -26, 0], [0, -49, 7, 91, -84, -84, 0, 0], [40, 2, 0, 0, 1, 2, 0, 2], [0, 0, 16, 0, -31, -31, 0, 0], [35, 0, 0, -35, 0, -26, -13, -2], [9, 0, 0, -9, 0, 18, 0, 36], [0, 0, 12, 0, 18, 18, 0, 0], [10, -16, 13, 0, -33, -16, 13, -16], [7, 70, 0, 0, 35, 70, 0, 70], [0, 0, -67, 0, 58, 0, -67, 0], [0, -20, -1, 41, -42, -42, 0, 0], [-13, 0, 0, 13, 0, -13, 0, -26], [0, 0, 0, 0, 0, 35, 9, 0], [0, -7, 22, -80, -51, -51, 0, 0], [-56, 10, 0, 0, 5, 10, 0, 10], [0, 0, 49, 0, -49, -49, 0, 0], [-9, -18, 18, 0, 27, -18, 18, -18], [0, 20, 0, -15, 10, 10, 0, 0]]}