# Stored data for newform 207.4.a.f, downloaded from the LMFDB on 20 January 2026.
{"Nk2": 3312, "analytic_conductor": 12.213395371188307, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [23, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [207, 1, [47, 28], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 1140200, "field_disc_factorization": [[2, 3], [5, 2], [5701, 1]], "field_poly": [25, 25, -20, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [48, 40, -27, -2, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998203961551, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "207.4.a.f", "level": 207, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 23], "level_radical": 69, "minimal_twist": "69.4.a.c", "nf_label": "4.4.1140200.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{2}+(6-\\beta _{1}-2\\beta _{2})q^{4}+(-1+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "207.4.a", "trace_display": [2, 0, 2, 32], "trace_hash": 1695813567351609367, "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "3.666", "prec": 17}, {"__RealLiteral__": 0, "data": "0.405", "prec": 17}, {"__RealLiteral__": 0, "data": "36.503", "prec": 20}, {"__RealLiteral__": 0, "data": "11.323", "prec": 20}, {"__RealLiteral__": 0, "data": "552.093", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 4, 2, 0, 26, 2, 0, 32, 18, 0, 150, -62, 0, 32, -180, 0, 258, 28, 0, 42, 490, 0, -322, 92, 0, 364, 336, 0, -260, 20, 0, 444, 506, 0, -700, -656, 0, 162, 354, 0, 998, 528, 0, 1230, 114, 0, 46, -36, 0, -8, 1482, 0, -712, -358, 0, 572, -2372, 0, 560, -892, 0, 294, -1004, 0, 762, 636, 0, -126, -1620, 0, -1348, -1032, 0, -1220, -430, 0, -1258, 932, 0, 1832, 2346, 0, -1092, -1178, 0, -3484, -458, 0, -5570, 872, 0, 496, 598, 0, -2408, 932, 0, -1324, 106, 0, 1386, 2276, 0, -668, -576, 0, 1142, -786, 0, 2926, -5068, 0, -2804, 6336, 0, 46, -7160, 0, -4024, 3356, 0, 3120, 1126, 0, 2188, -1908, 0, 2728, 6178, 0, 420, 620, 0, 1712, -5006, 0, -5228, -68, 0, 3160, -7244, 0, -3432, 204, 0, -5820, 472, 0, 4390, -3126, 0, 2012, -3918, 0, 2812, -2880, 0, 3922, -3356, 0, 13094, 736, 0, 1356, 17884, 0, -4718, -136, 0, -2412, -6472, 0, 15586, 11068, 0, -4608, -10702, 0, -4976, -8280, 0, 3302, 6480, 0, 414, 7344, 0, -1192, 8296, 0, -1776, 2316, 0, 1636, 5248, 0, 3858, 720, 0, 648, 27178, 0, 18264, 2240, 0, 4772, -7624, 0, -4696, 3680, 0, 3332, -8454, 0, -17838, 324, 0, 8240, 8102, 0, -30564, -2616, 0, -3788, -9396, 0, 840, -3478, 0, 5078, 3450, 0, 3600, 7424, 0, -448, -13992, 0, 3448, -13416, 0, 1956, -1618, 0, -622, 3866, 0, 10636, -9228, 0, 10100, 2598, 0, -1426, 10432, 0, -8910, -4560, 0, 6364, -420, 0, -2308, -9192, 0, -1112, 12004, 0, 7542, -5152, 0, 880, -8596, 0, -5572, -38602, 0, -220, 17280, 0, -31092, -2768, 0, -17146, -12776, 0, 8724, -5488, 0, -4848, -6780, 0, 1776, 2, 0, -21872, -23662, 0, -7682, 736, 0, 4064, 4292, 0, -12762, 1640, 0, 2036, 37156, 0, 6312, 21188, 0, 1820, -25710, 0, 18452, 5388, 0, -20500, 32426, 0, -4140, -3172, 0, -3448, 21244, 0, 19100, -368, 0, -11916, -37314, 0, 23272, 3556, 0, -11200, 1534, 0, -20136, 856, 0, -13640, 18822, 0, 23144, -9616, 0, -3556, -23700, 0, -9282, 9824, 0, -19048, 3312, 0, 7500, -6828, 0, -8148, 15462, 0, -13760, -2316, 0, -15232, 5934, 0, -2648, -1872, 0, -1846, 16488, 0, -4952, 11640, 0, -494, -14768, 0, 8084, 26928, 0, 38808, -30916, 0, 16264, -4682, 0, 644, 1994, 0, -16276, -6168, 0, -18608, -26884, 0, 61218, -34684, 0, -1688, 6032, 0, 30800, 39352, 0, 7804, 45772, 0, 34208, 3408, 0, -24652, 7248, 0, 16080, -11698, 0, 11226, -33308, 0, 70, 2708, 0, 2260, -11874, 0, 60936, 10436, 0, 30284, -19448, 0, 31746, 966, 0, -680, -39020, 0, 4440, -6312, 0, -7388, 22996, 0, -29124, 10840, 0, -5276, 55160, 0, -26082, 11592, 0, 6788, 42606, 0, 11270, -13120, 0, -1768, -17960, 0, 24076, 4246, 0, 17256, 1880, 0, -11912, -26456, 0, -21138, 36664, 0, -3832, -13264, 0, 15196, -3800, 0, -9394, 20908, 0, -49352, 1862, 0, 6910, -33776, 0, 18800, 15252, 0, 13900, -1648, 0, 10228, 95180, 0, 6858, -6572, 0, 24260, -7406, 0, 3856, -25244, 0, -31976, -13430, 0, -55396, 20896, 0, 14728, -1868, 0, -14556, 22308, 0, 6754, -10604, 0, -55336, 18280, 0, 2116, -17812, 0, -3748, -45936, 0, -68268, -65630, 0, 15676, 7514, 0, 24340, -11352, 0, -50604, 25896, 0, -34164, -37276, 0, -26582, 12940, 0, 21252, 65616, 0, 26960, 5678, 0, -26060, -99372, 0, -41384, -17862, 0, 20452, 48510, 0, -4360, -17252, 0, 16810, -24468, 0, -113208, 8372, 0, 53632, 11486, 0, 13500, 33708, 0, -4364, 58552, 0, -6498, 19644, 0, 888, -60424, 0, -24234, 24760, 0, 2328, 13954, 0, 7728, -37744, 0, 62896, -110804, 0, 13676, -66966, 0, -12796, 3970, 0, 10432, -37488, 0, 40110, -3652, 0, 15100, -50976, 0, 28030, 5976, 0, 32768, 32452, 0, 73724, -808, 0, 41030, -20024, 0, -62164, -9868, 0, -11040, -880, 0, -4464, 75380, 0, 3558, -14244, 0, 58142, -5980, 0, 14976, -14164, 0, -16280, -33384, 0, -59388, 21956, 0, -5376, 121708, 0, -54000, -7698, 0, -11466, 17596, 0, -97870, 34672, 0, 460, 47016, 0, -39544, -5824, 0, -5216, -100444, 0, -51898, 19314, 0, -58832, -117848, 0, -27704, 16012, 0, -69180, 45640, 0, 137266, 20076, 0, 31076, 80432, 0, -41868, 31960, 0, -10952, -21452, 0, -173940, 37462, 0, 40852, -42126, 0, 91356, -39720, 0, 20034, -56408, 0, -66208, 10212, 0, 5496, 9780, 0, 95724, 32412, 0, -1844, 21678, 0, -47774, 75500, 0, -2848, -5136, 0, 4076, 10516, 0, -25022, 11052, 0, 11638, 90792, 0, 104520, -87224, 0, 53468, -26456, 0, 33464, 64730, 0, 136824, 31932, 0, -36636, 32808, 0, -24120, -3792, 0, 69734, -39518, 0, -51808, 37368, 0, -7764, -126628, 0, -31336, -41136, 0, 31700, 94088, 0, 6332, -2274, 0, 4884, 107712, 0, -19974, -79420, 0, -17096, -16100, 0, 14394, -82736, 0, -32338, -50548, 0, 56644, 59812, 0, 18052, 3460, 0, -5412, 65846, 0, 7528, 69186, 0, 45724, -46396, 0, -15088, 54168, 0, 173848, 15376, 0, 7484, -63200, 0, -37928, 17200, 0, -50592, -54212, 0, 149876, 56668, 0, -8172, -57656, 0, 41456, 40118, 0, -60828, -147332, 0, 61016, -14116, 0, 61432, -14560, 0, 58634, 5472, 0, 25484, -53310, 0, 102076, 24094, 0, 18424, -48678, 0, -104660, 3726, 0, 13296, 7132, 0, -55662, 67568, 0, 2216, 216408, 0, 42164, 33364, 0, 66324, -47440, 0, 54936, -10500, 0, -13508, 79206, 0, 8142, -117256, 0, -55748, 41960, 0, -106308, 744, 0, 34964, -14040, 0, 64944, 19068, 0, -9480, -22136, 0, -47972, -56088, 0, 67800, 40028, 0, -135700, -9160, 0, -2588, -208036, 0, -24296, -9512, 0, 35782, 76354, 0, 8136, -42236, 0, 58196, 140952, 0, -30502, 35624, 0, -8424, 22954, 0, -46748, -43296, 0, -170698, -32224, 0, -76640, -28632, 0, -5894, 95548, 0, -88054, 185152, 0, -43064, -17084, 0, -16920, -74294, 0, 12144, -69288, 0, -189656, 30816, 0, -68360, -75266, 0, 101992, 12652, 0, -80360, -130056, 0, -61688, 16020, 0, -42812, 90660, 0, -199520, -85220, 0, 85644, 115422, 0, 62220, 19114, 0, -40320, -80768, 0, 4610, -13796, 0, 53320, 9890, 0, -9220, -63868, 0, -47972, 55640, 0, -5444, 28290, 0, 20020, -1228, 0, 38352, -88832, 0, -69404, 24036, 0, 128948], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [6, -1, -2, 0], [-1, -3, -2, -1], [0, 0, 0, 0], [10, 4, 1, -1], [0, -9, 0, 4], [0, 0, 0, 0], [33, -9, -3, 2], [-13, 5, -5, -6], [0, 0, 0, 0], [6, -4, 2, -4], [-44, 2, 8, -4], [0, 0, 0, 0], [58, -13, -6, 8], [14, 14, 7, 3], [0, 0, 0, 0], [9, -3, 2, -9], [103, -39, -1, 18], [0, 0, 0, 0], [-75, 11, 21, -2], [23, 0, 0, 0], [0, 0, 0, 0], [79, -24, 18, 28], [90, 12, -6, -12], [0, 0, 0, 0], [-32, 66, -8, -16], [4, -2, 32, 10], [0, 0, 0, 0], [122, 22, 0, -2], [100, -53, -28, -4], [0, 0, 0, 0], [-162, 26, 18, -8], [-152, 24, -4, -30], [0, 0, 0, 0], [45, 9, -31, -40], [101, 25, 1, -22], [0, 0, 0, 0], [185, -129, -71, 22], [134, 4, -44, 24], [0, 0, 0, 0], [311, 7, -18, 25], [107, 157, 43, 2], [0, 0, 0, 0], [0, -23, 0, 0], [6, 30, -30, 10], [0, 0, 0, 0], [-5, -6, -16, -4], [322, -97, -94, 20], [0, 0, 0, 0], [-198, -40, 26, 20], [-97, -15, 22, -5], [0, 0, 0, 0], [206, 126, 142, 52], [-548, 90, 92, 16], [0, 0, 0, 0], [202, 124, -46, -44], [-190, 66, 46, 46], [0, 0, 0, 0], [67, -13, 7, -8], [-298, -94, 46, -4], [0, 0, 0, 0], [102, -177, -26, -16], [162, 6, 6, -24], [0, 0, 0, 0], [9, 81, -64, -59], [-310, 190, -14, -76], [0, 0, 0, 0], [-214, 246, 82, -52], [-232, 52, 40, 48], [0, 0, 0, 0], [-324, -38, 2, 80], [-143, -71, 89, -18], [0, 0, 0, 0], [-305, 19, 55, 26], [198, -70, -138, -60], [0, 0, 0, 0], [490, 64, -23, 15], [375, -423, -201, 42], [0, 0, 0, 0], [-484, -422, 28, 136], [-239, 111, 77, -58], [0, 0, 0, 0], [-826, 90, -68, -116], [-349, -469, 7, 86], [0, 0, 0, 0], [-1307, 171, 101, -66], [268, 100, -19, -45], [0, 0, 0, 0], [84, -80, 40, -68], [138, -23, -46, 0], [0, 0, 0, 0], [-680, -156, 80, 80], [266, 66, 58, -34], [0, 0, 0, 0], [-400, -138, -48, 78], [-8, -69, 8, 24], [0, 0, 0, 0], [-32, -757, -264, 4]]}