# Stored data for newform 21.4.g.a, downloaded from the LMFDB on 25 April 2024.
{"label": "21.4.g.a", "space_label": "21.4.g", "level": 21, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 412383969301, "dim": 12, "is_polredabs": true, "trace_hash": 1661188859105587163, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(\\beta _{2}-\\beta _{6})q^{2}+(\\beta _{7}+\\beta _{8})q^{3}+(-2\\beta _{4}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "g", "char_is_real": false, "Nk2": 336, "analytic_conductor": 1.2390401101205528, "hecke_ring_index": 27, "level_radical": 21, "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": "0.590", "prec": 17}, "analytic_rank_proved": true, "char_values": [21, 6, [8, 10], [3, 5]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [5, 17], "field_disc": 1666117098337039248466944, "field_disc_factorization": [[2, 10], [3, 6], [7, 6], [2087, 4]], "field_poly": [531441, -59049, 0, -21141, 486, -441, 1564, -49, 6, -29, 0, -1, 1], "hecke_ring_index_factorization": [[3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "10.564", "prec": 20}, {"__RealLiteral__": 0, "data": "11.134", "prec": 20}, {"__RealLiteral__": 0, "data": "1047.143", "prec": 27}, {"__RealLiteral__": 0, "data": "3712.887", "prec": 27}, {"__RealLiteral__": 0, "data": "200087.822", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "3.2.3.c6", "trace_display": [0, -3, 0, -56], "traces": [0, 12, 0, -3, 14, 0, 0, -56, 0, -3, 30, 0, -192, 0, 0, 6, 134, 0, 66, 300, 0, 357, -268, 0, 414, -42, 0, 0, -602, 0, -822, -930, 0, -855, 0, 0, 852, 764, 0, -426, 2298, 0, 966, -1012, 0, 2367, 608, 0, 0, -336, 0, -1341, -3000, 0, -4158, 0, 0, 270, 2870, 0, -918, 2358, 0, 1071, -548, 0, 2934, 792, 0, 0, -4242, 0, -2712, -2904, 0, -2418, 0, 0, 4296, 1674, 0, 837, 5040, 0, 3864, 348, 0, 1638, -554, 0, 0, -1218, 0, -1479, -1356, 0, -4410, 0, 0, -3354, 968, 0, -270, 888, 0, 1302, -9172, 0, 180, -3184, 0, 0, 2016, 0, -18, 30, 0, 4122, 0, 0, 2640, -1498, 0, -210, 2766, 0, -546, 13968, 0, -174, 6060, 0, 0, 84, 0, 1638, 7716, 0, -1854, 0, 0, -7386, -2800, 0, -990, -13566, 0, -10563, -6640, 0, -7740, 428, 0, 0, 770, 0, 7044, -4794, 0, 15273, 0, 0, 6516, -5550, 0, 3489, -11970, 0, -4746, 9024, 0, -1449, -6580, 0, 0, 19180, 0, 8277, 21576, 0, 10908, 0, 0, -14850, -4052, 0, 192, -16998, 0, -5418, -3936, 0, -19680, 1142, 0, 0, 1400, 0, 4728, 9990, 0, 21777, 0, 0, 6480, -11676, 0, 2649, 1716, 0, 546, 11840, 0, -6426, -5818, 0, 0, -3864, 0, 7929, -7290, 0, 2862, 0, 0, -19812, -15064, 0, -1224, -21456, 0, -11697, 9100, 0, -24624, -10326, 0, 0, 16884, 0, 3882, 20364, 0, 9747, 0, 0, 13272, -306, 0, 6510, 20442, 0, -4326, 16028, 0, 11439, 19726, 0, 0, 7056, 0, 11928, 34302, 0, -11304, 0, 0, -24606, 8248, 0, -3060, -16752, 0, 7056, -45376, 0, 2088, -10800, 0, 0, -34020, 0, -8970, -60696, 0, 2925, 0, 0, 32256, 4956, 0, -4164, -18108, 0, 10878, 28488, 0, 7182, -3592, 0, 0, 27174, 0, -13353, 7932, 0, -23850, 0, 0, -11322, 16458, 0, 2148, 13530, 0, -13923, -21284, 0, 21582, 31598, 0, 0, -31024, 0, -16974, 13926, 0, 14889, 0, 0, 28536, 4964, 0, 3897, 74844, 0, 17304, 13016, 0, 39564, -6372, 0, 0, -28616, 0, -15123, -79980, 0, -51282, 0, 0, 1620, 2730, 0, -15726, -7140, 0, 16947, -39496, 0, 23850, -35166, 0, 0, 53508, 0, -13962, -20166, 0, -34398, 0, 0, 96, 28596, 0, -11841, 55848, 0, 42588, -19324, 0, -11094, 43532, 0, 0, -41874, 0, -17226, 29298, 0, -53856, 0, 0, -14862, 23660, 0, -13140, 52296, 0, -1890, -23128, 0, 18810, 2550, 0, 0, -75544, 0, -15480, -47214, 0, -225, 0, 0, 35076, 8778, 0, 28512, -2760, 0, 18774, 41436, 0, 42057, -29198, 0, 0, 59094, 0, -13308, -15312, 0, -3384, 0, 0, 31920, 32048, 0, 2250, -13812, 0, 25935, 42192, 0, 6168, 35202, 0, 0, -64806, 0, -8952, 17388, 0, -48741, 0, 0, 13320, -26914, 0, -9828, 37692, 0, -16926, -33156, 0, -24975, -36016, 0, 0, -86254, 0, 7131, -89430, 0, -9360, 0, 0, -46194, 16436, 0, 11088, -15906, 0, -16926, -56480, 0, -12312, -13810, 0, 0, 128772, 0, 8064, 63924, 0, 38079, 0, 0, 6384, 16388, 0, 1680, -60354, 0, 4200, -7884, 0, 51819, 71050, 0, 0, 39774, 0, 7344, 118848, 0, 48588, 0, 0, 48306, -35292, 0, 1218, 45576, 0, 22050, 36776, 0, -23022, -44380, 0, 0, -6552, 0, 13626, -144996, 0, 34299, 0, 0, -94500, -37848, 0, -54018, -69804, 0, -54852, 21192, 0, -78309, -42436, 0, 0, 63560, 0, 20037, 73776, 0, 48798, 0, 0, -6714, -32452, 0, 2484, 3696, 0, -78687, 51184, 0, -31086, 97224, 0, 0, -37464, 0, 20934, 141282, 0, 20685, 0, 0, -75252, -34924, 0, 41544, -64134, 0, -50484, -40872, 0, -25452, -27684, 0, 0, 2436, 0, 50811, -82008, 0, 78444, 0, 0, 71670, -81226, 0, 42402, -134394, 0, 59934, 111144, 0, 9396, -83670, 0, 0, 144298, 0, 55254, 65220, 0, -27972, 0, 0, 2448, 31998, 0, -22095, -36000, 0, -47502, -79692, 0, -132852, 55670, 0, 0, -37842, 0, 13566, 143670, 0, 162450, 0, 0, -4776, -8772, 0, 25560, 50664, 0, -41643, 71704, 0, -66366, -15660, 0, 0, -60228, 0, 29772, 60600, 0, 20592, 0, 0, -91596, -4900, 0, 31830, -203712, 0, -31500, -46456, 0, 34326, -64414, 0, 0, 109326, 0, 17265, -32982, 0, 17604, 0, 0, -70878, -18408, 0, -7446, -20028, 0, 70140, 96248, 0, -39312, 16380, 0, 0, -32228, 0, 74340, 53508, 0, -14013, 0, 0, 7236, -51862, 0, -19959, -74940, 0, -3906, -72888, 0, -87066, -28120, 0, 0, -153552, 0, -66789, -160164, 0, 59148, 0, 0, 173556, -75732, 0, -15924, 110508, 0, -88788, 94584, 0, 18900, 61860, 0, 0, 224966, 0, -318, 185754, 0, 6804, 0, 0, -94380, 28190, 0, 44226, 229068, 0, -29232, 86096, 0, 36891, 35076, 0, 0, 58170, 0, 14157, 12000, 0, -38832, 0, 0, 68298, 66446, 0, -35400, 40314, 0, 85344, -102160, 0, 96660, -29764, 0, 0, -74074, 0, -49962, -291654, 0, -164529, 0, 0, -155604, 5112, 0, -93027, -116220, 0, 18522, -143796, 0, -68697, -124804, 0, 0, -67998, 0, -36747, 15024, 0, 49680, 0, 0, 111570, 20320, 0, 19260, -9102, 0, -9702, 53424, 0, 184374, 138594, 0, 0, -40866, 0, -39780, 33384, 0, -65415, 0, 0, -33504, 81564, 0, 15660, -36036, 0, 36624, -187336, 0, 131544, 61208, 0, 0, 30394, 0, 621, -123672, 0, 39312, 0, 0, 68130, 88054, 0, 46416, 159270, 0, 142674, 118760, 0, 4158, -74586, 0, 0, 8232, 0, -102270, 23550, 0, -143550, 0, 0, 107280, 49806, 0, -82236, 104862, 0, 20874, 38804, 0, -49545, 113630, 0, 0, -268996, 0, -106425, -117954, 0, -174978, 0, 0, 22944, 45332, 0, 28896, 219882, 0, -79128, -105392, 0, 146196, 2444, 0, 0, -71484, 0, 15048, -56574, 0, -104301, 0, 0, 53352, 82412, 0, 78996, -82152, 0, 53046, -30580, 0, 143451, -38346, 0, 0, -3066, 0, -19065, -16728, 0, -112320, 0, 0, 241098, 36864, 0, 21738, 26460, 0, 177408, -45056, 0, 33720, -47178, 0, 0, -32172, 0, -105396, -159486, 0, -65016, 0, 0, -198444, -94680, 0, -122343, 161022, 0, 55650, 16992, 0, -86157, -2046, 0, 0, -152670, 0, -1398, -36336, 0, -79038, 0, 0, -64746, 18746, 0, -76272, 145572, 0, -48300, -47160, 0, 34254, 97154, 0, 0, 22232, 0, -26082, 99576, 0, -49176, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 21, 7, 1, 6, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "21.4.g.a", "char_is_minimal": true, "conrey_index": 5, "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], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [2, 0, -1, -1, 4, -1, 2, -1, 0, 1, -1, 0], [-5, 0, 0, 3, -1, 0, 0, -1, -1, 0, -1, 3], [0, 1, -2, 0, 0, -1, 0, -1, -2, -1, 0, 1], [0, 1, 0, -3, 0, 1, 0, -1, 1, -2, 0, -2], [0, -6, 0, -2, 0, 0, 0, -5, -4, 0, 1, -1], [0, 2, 0, 0, 0, -2, 4, -2, 2, 1, 0, -4], [-10, 2, -4, 2, 10, 1, -4, -2, -1, 0, -4, 5], [-9, 2, 0, 3, -18, 0, 0, 5, 0, 0, 3, -2], [0, -4, -10, 0, 0, 1, 9, 4, -1, 2, 0, 5], [3, 4, 12, 0, 0, 1, 0, 1, 2, 1, 0, 4], [24, 3, 0, -1, 24, 0, 0, 3, 2, 0, 0, -2], [0, -9, 8, 0, 0, 0, -4, 9, 9, 0, 0, 0], [0, 6, 0, 0, -6, 0, -3, 6, 0, 0, 6, -18], [17, 1, 0, 1, -17, 0, 0, -1, 0, 0, -2, 2], [0, 3, 12, 0, 0, 3, -24, -3, 0, -3, 0, -3], [13, -16, 16, -5, -31, -3, -20, -1, 0, 1, 4, 8], [-16, 3, 0, -5, 0, 0, 0, 8, 16, 0, 5, 3], [0, 10, 4, 0, 0, 0, -4, -10, -5, 0, 0, -5], [40, -10, -20, 10, 20, 0, 10, -3, -8, -2, -5, 5], [0, 11, 0, 0, 13, 0, 0, -4, -11, 0, -15, -7], [0, 0, 19, 0, 0, -7, 19, 0, -9, 0, 0, 9], [21, 0, -24, 3, 42, 3, 48, -3, 0, -3, 3, 0], [-6, -7, 0, -9, 80, 0, 0, -11, 10, 0, -4, 12], [0, 7, -52, 0, 0, 5, 0, -7, -14, 5, 0, 7], [-138, 4, -12, 18, -138, -5, 12, 4, -7, 10, 0, 7], [-110, -12, 0, -4, -55, 0, 0, -10, -8, 0, 2, -2], [0, 9, 0, 0, 0, 10, 0, -9, 9, -5, 0, -18], [-49, -10, -16, -10, 49, -5, -16, 10, 7, 0, 20, -16], [-4, 4, 0, -14, -8, 0, 0, -10, 0, 0, -14, -4], [0, -9, -12, 0, 0, -3, 36, 9, 3, -13, 0, 6], [66, -1, 48, 3, 0, -4, 0, -8, -16, -4, -3, -1], [135, 19, 0, 11, 135, 0, 0, 19, 4, 0, 0, -4], [0, -3, 26, 0, 0, 0, -13, 3, 3, 3, 0, 0], [0, -5, 0, 0, 63, 4, -36, -16, 1, -2, -15, 25], [132, -13, 0, -13, -132, 0, 0, 13, 26, 0, 26, 0], [0, -6, 32, 0, 0, -16, -64, 6, 0, 16, 0, 6], [14, 30, 47, 14, -140, 17, -43, 5, -3, -8, -7, -6], [-87, 18, 0, 31, 0, 0, 0, -13, -26, 0, -31, 18], [0, -22, -12, 0, 0, -3, 12, 22, 11, 6, 0, 11], [270, 0, 0, -30, 135, 0, 0, 6, 21, 12, 15, -15], [0, -10, 0, 0, -100, 0, 0, 24, 10, 0, 34, -14], [0, 0, 20, 0, 0, 14, 20, 0, 27, 0, 0, -27], [44, 9, -4, -4, 88, 5, 8, 19, 0, -5, -4, -9], [42, -21, 0, -7, 175, 0, 0, 14, -21, 0, 35, -42], [0, -15, -7, 0, 0, -7, 0, 15, 30, -7, 0, -15], [-219, 5, -12, -39, -219, 5, 12, -13, 13, -10, 0, -22], [-308, 58, 0, 40, -154, 0, 0, 38, 18, 0, -20, 20], [0, -28, 0, 0, 0, -6, 40, 28, -28, 3, 0, 56], [-228, 15, -21, 15, 228, 3, -21, -15, -15, 0, -30, 33], [-150, -28, 0, 19, -300, 0, 0, -9, 0, 0, 19, 28], [0, 45, -66, 0, 0, -6, 2, -45, -15, 23, 0, -30], [30, -7, 12, -6, 0, -1, 0, 20, 40, -1, 6, -7], [436, -93, 0, -25, 436, 0, 0, -93, -34, 0, 0, 34], [0, 54, -32, 0, 0, 0, 16, -54, -54, -19, 0, 0], [0, -6, 0, 0, 144, -24, 72, -21, -6, 12, -27, 39], [114, 38, 0, 38, -114, 0, 0, -38, -89, 0, -76, -13], [0, 6, -31, 0, 0, 22, 62, -6, 0, -22, 0, -6], [-45, 23, -72, 6, -282, -25, 48, -11, 23, 20, -30, -7], [-84, -79, 0, -61, 0, 0, 0, -18, -36, 0, 61, -79], [0, 12, 84, 0, 0, 14, -84, -12, -6, -28, 0, -6], [332, 25, -40, -28, 166, 0, 20, -21, -7, -19, 14, -14], [0, -62, 0, 0, -181, 0, 0, -23, 62, 0, 39, 85], [0, 0, -48, 0, 0, 6, -48, 0, -30, 0, 0, 30], [143, -15, -4, 11, 286, -19, 8, 11, 0, 19, 11, 15], [-252, 119, 0, 49, 168, 0, 0, 63, 0, 0, -56, -14], [0, -18, 68, 0, 0, 4, 0, 18, 36, 4, 0, -18], [-456, -54, 66, 24, -456, 9, -66, 54, 15, -18, 0, 39], [-290, 38, 0, -22, -145, 0, 0, 49, 60, 0, 11, -11], [0, -11, 0, 0, 0, -38, -67, 11, -11, 19, 0, 22], [-147, 3, 60, 3, 147, 18, 60, -3, -1, 0, -6, -75], [18, 6, 0, 12, 36, 0, 0, 18, 0, 0, 12, -6], [0, -15, 148, 0, 0, 23, -52, 15, 54, 18, 0, -39], [336, -57, -141, -30, 0, 21, 0, 3, 6, 21, 30, -57], [325, 88, 0, -12, 325, 0, 0, 88, 50, 0, 0, -50], [0, 15, 72, 0, 0, 0, -36, -15, -15, 37, 0, 0], [0, -57, 0, 0, -144, 42, -72, 75, 6, -21, 81, 33], [296, -4, 0, -4, -296, 0, 0, 4, 52, 0, 8, 44], [0, -27, -56, 0, 0, 13, 112, 27, 0, -13, 0, 27], [220, 13, -20, -20, -166, -19, 88, 17, -56, -3, 58, -59], [54, 17, 0, -12, 0, 0, 0, 29, 58, 0, 12, 17], [0, -62, -133, 0, 0, -5, 133, 62, 31, 10, 0, 31], [200, 112, 224, 146, 100, 0, -112, 15, -58, -16, -73, 73], [0, 74, 0, 0, 124, 0, 0, -53, -74, 0, -127, -21], [0, 0, -104, 0, 0, -48, -104, 0, 51, 0, 0, -51], [-18, -15, 144, -3, -36, -6, -288, -108, 0, 6, -3, 15], [143, -77, 0, -55, 499, 0, 0, -75, 9, 0, 2, 29], [0, -6, 144, 0, 0, -14, 0, 6, 12, -14, 0, -6], [-276, 8, -24, 36, -276, -10, 24, -102, -69, 20, 0, 14], [-184, -98, 0, -96, -92, 0, 0, -50, -2, 0, 48, -48], [0, -3, 0, 0, 0, 32, 36, 3, -3, -16, 0, 6], [-228, -27, 60, -27, 228, -12, 60, 27, 42, 0, 54, 60], [-156, 37, 0, -81, -312, 0, 0, -44, 0, 0, -81, -37], [0, 42, 63, 0, 0, 7, -140, -42, -63, -84, 0, 21], [-303, 75, -132, 87, 0, -18, 0, -93, -186, -18, -87, 75], [146, -16, 0, 44, 146, 0, 0, -16, -30, 0, 0, 30]]}