# Stored data for newform 207.4.a.b, downloaded from the LMFDB on 16 July 2025.
{"Nk2": 3312, "analytic_conductor": 12.213395371188307, "analytic_rank": 1, "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": 2, "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 8, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-7, -2, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599694479567, "hecke_ring_generator_nbound": 2, "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.b", "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.b", "nf_label": "2.2.8.1", "prim_orbit_index": 1, "qexp_display": "q+(1+\\beta )q^{2}+(1+2\\beta )q^{4}+(-4-4\\beta )q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "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, -8, -28], "trace_hash": 259754193444570714, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "10.191", "prec": 20}, {"__RealLiteral__": 0, "data": "1.947", "prec": 17}, {"__RealLiteral__": 0, "data": "73.820", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, 2, 0, 2, -8, 0, -28, 18, 0, -72, 72, 0, -60, -44, 0, -78, -96, 0, -148, -136, 0, 184, -46, 0, 38, -156, 0, -60, 204, 0, -168, -414, 0, -176, 176, 0, 116, -532, 0, 248, -4, 0, -420, 296, 0, -46, 48, 0, -278, 550, 0, -252, -32, 0, -736, -172, 0, 1260, 40, 0, -764, 696, 0, 34, 624, 0, -988, -256, 0, 1136, 224, 0, 820, 804, 0, -916, -1120, 0, 1772, 1080, 0, 412, -1480, 0, 704, -132, 0, 88, -744, 0, 936, -46, 0, 1456, 2128, 0, -260, 170, 0, 1062, -1644, 0, -148, -60, 0, 128, 696, 0, -228, -3488, 0, 1284, -584, 0, 184, 2316, 0, -2488, 1424, 0, 714, 20, 0, 1560, -1200, 0, -1096, 1394, 0, 2928, 3912, 0, 2456, 1348, 0, -464, -3704, 0, -1256, 2096, 0, -4352, -2832, 0, -5040, 1716, 0, 1492, 1272, 0, -1712, 588, 0, -3264, -2784, 0, -1340, 828, 0, 2360, 644, 0, 368, 828, 0, -4856, 1200, 0, -2018, 4096, 0, 156, -3284, 0, -1044, -4152, 0, 3272, -3432, 0, -388, 2760, 0, -414, -3216, 0, -4016, 2864, 0, 8400, 2952, 0, 1196, -7556, 0, 618, 2940, 0, -500, -2218, 0, 340, -3912, 0, -1648, -6116, 0, 3492, -8016, 0, -4448, 288, 0, -2424, 528, 0, 1488, -10548, 0, -6240, 3360, 0, 608, 5972, 0, -8344, -2864, 0, 3180, 1656, 0, -3444, 716, 0, -5824, -5016, 0, 3312, 10064, 0, 7500, 8778, 0, 804, -680, 0, 6744, -5832, 0, 3536, 14352, 0, -1656, -2152, 0, 850, 1980, 0, -2312, 5232, 0, 9000, -4920, 0, -512, 9016, 0, 3684, 13100, 0, 6088, 4704, 0, -1320, 4952, 0, -5828, 3928, 0, -3216, -3736, 0, -5724, -8928, 0, -9648, -360, 0, -4818, -15792, 0, 2612, -7968, 0, 9952, -2396, 0, 8632, 1380, 0, 5592, 13584, 0, 10380, -80, 0, 1792, -5408, 0, -864, -416, 0, -1148, 2740, 0, -116, 3756, 0, 14736, 7672, 0, 1012, 9024, 0, -4212, -4112, 0, -2116, -2080, 0, -1424, -8232, 0, 16208, -5392, 0, 428, 3742, 0, 7488, 0, 0, 13048, -5220, 0, -5172, 4216, 0, -6092, -8516, 0, -16136, -8732, 0, 17408, 7288, 0, -17832, 2888, 0, 6450, 12268, 0, 4584, -6864, 0, 10796, 1794, 0, -9680, 288, 0, -5548, -12272, 0, -6608, -12456, 0, 220, 14672, 0, -4984, 872, 0, 13056, -3476, 0, -14852, 10800, 0, 2208, -4742, 0, -8644, -3312, 0, -3220, -24932, 0, -7626, -1008, 0, -144, 2324, 0, -20328, 8992, 0, -17732, -3184, 0, -12084, 1968, 0, 19424, 13476, 0, -30128, 12504, 0, -1300, -2144, 0, -1088, -4384, 0, 9912, -5544, 0, 12816, -9440, 0, -24284, -9264, 0, -20868, 3404, 0, 14928, 7136, 0, 10368, 6840, 0, -13088, 18656, 0, 1476, 5004, 0, 2768, -16104, 0, -672, -11040, 0, -31092, 6300, 0, 3128, -8964, 0, 7088, -20628, 0, -5364, -8432, 0, 11496, -12992, 0, 13000, -13104, 0, -15100, 5200, 0, 1488, -4672, 0, -7608, 18444, 0, 16842, 30224, 0, 30128, -10796, 0, 6424, -5352, 0, -15072, 25368, 0, -3816, 1440, 0, 3376, 8272, 0, 13056, -32256, 0, -1360, -4232, 0, -3208, -19428, 0, -12376, 16194, 0, 6428, 24464, 0, 11584, -12872, 0, -5904, 10200, 0, 16260, 14088, 0, 8360, 3744, 0, 1058, -128, 0, 15576, -2376, 0, 9696, -20572, 0, 9516, -6872, 0, -28908, -16856, 0, 20752, 42192, 0, -12640, 1064, 0, 25512, -40440, 0, -23864, -9892, 0, 9112, -22416, 0, 10872, -18384, 0, -17960, 13872, 0, 33376, -4764, 0, 24896, 37184, 0, 7380, -16464, 0, -6152, -874, 0, -12932, 2862, 0, -26544, 24096, 0, -32, 2900, 0, -8192, 44952, 0, -8304, 18784, 0, -12780, 21660, 0, -13248, 15992, 0, 3588, 4736, 0, 9196, 4920, 0, 28880, -35112, 0, 17072, 34860, 0, 21232, -9888, 0, -6236, 26112, 0, 640, -18744, 0, 27108, 1056, 0, -30016, 6400, 0, -18894, -39708, 0, 6820, -9008, 0, -27380, 20668, 0, 42828, 8608, 0, 5652, 64176, 0, -4488, 7264, 0, -18292, 1380, 0, 33376, -52272, 0, -16256, -21396, 0, -8592, 41668, 0, -36000, -4836, 0, -22176, 46864, 0, 16724, -42640, 0, 3560, -36064, 0, -4692, 31216, 0, 16880, -22016, 0, -46164, -32308, 0, 9502, -15240, 0, 10936, -10624, 0, 21696, -27224, 0, 5280, 14488, 0, 12924, 0, 0, 29456, -7060, 0, 37944, -15712, 0, -1888, -47372, 0, -15988, -26616, 0, -25096, -12440, 0, 29124, 21032, 0, 24172, 28544, 0, -26776, 3864, 0, 38592, -32232, 0, 13576, -4800, 0, 8040, 63282, 0, 24924, 37668, 0, 17652, -696, 0, -36688, 18720, 0, -14356, 18748, 0, 9522, -19216, 0, -10664, -16144, 0, -1696, -13512, 0, -34528, 13700, 0, -20528, -6624, 0, 9700, -18768, 0, -53928, -54336, 0, 20924, 18204, 0, -12208, -23916, 0, 13512, -12920, 0, 9096, 13968, 0, -40044, 57472, 0, -8148, -31016, 0, 24456, 34140, 0, -16528, -9688, 0, -23968, 4048, 0, 5466, -10960, 0, -36500, -20228, 0, -56240, 15936, 0, 18216, 29036, 0, -49364, -30384, 0, -9344, -13498, 0, -20032, 35792, 0, -4048, -18000, 0, -24716, -37068, 0, -33152, -36744, 0, 40256, 16448, 0, 24168, -56004, 0, -4720, 28740, 0, -71400, 28508, 0, 37040, -4224, 0, 15924, 80288, 0, 10692, 11104, 0, -64832, -52240, 0, -2712, 24, 0, 41726, 62204, 0, 160, -14968, 0, -18060, -672, 0, -30480, -2668, 0, -53124, 5048, 0, 21864, -14628, 0, 9832, 25104, 0, -22144, 43296, 0, 20688, -46524, 0, -20016, 57184, 0, 15624, 49548, 0, 12236, 12064, 0, 84668, -30768, 0, 61728, -54600, 0, -52912, 17376, 0, -11016, -10896, 0, 16400, -5344, 0, 36704, -37344, 0, 71328, -19244, 0, -18452, 39888, 0, 736, 17520, 0, 33544, -49072, 0, -41004, 1520, 0, -48288, -16272, 0, -76912, -34740, 0, 9420, -59856, 0, 23484, -5704, 0, -16324, 20736, 0, 24220, -34192, 0, -53844, -12660, 0, 9820, -11444, 0, 63168, 49088, 0, 34660, -13304, 0, -20160, -3096, 0, 92, 28776, 0, -26256, 30040, 0, -29976, -60284, 0, 3376, -30928, 0, 19936, -7088, 0, 14208, 49472, 0, 1186, -33816, 0, 29388, 13904, 0, 51480, -33894, 0, 67728, -19344, 0, 12400, 22640, 0, 20388, -936, 0, 1328, 13528, 0, 70360, -28032, 0, 34576, -73920, 0, 43992, 9660, 0, 35592, 25272, 0, 63712, 99728, 0, -28508, 48304, 0, -34480], "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], [1, 0], [1, 1], [0, 0], [1, 2], [-4, -4], [0, 0], [-14, -1], [9, -5], [0, 0], [-36, -8], [36, 7], [0, 0], [-30, -6], [-22, -15], [0, 0], [-39, -12], [-48, -5], [0, 0], [-74, -24], [-68, -12], [0, 0], [92, 43], [-23, 0], [0, 0], [19, 32], [-78, -36], [0, 0], [-30, -29], [102, 66], [0, 0], [-84, 54], [-207, -11], [0, 0], [-88, -53], [88, 60], [0, 0], [58, 43], [-266, -98], [0, 0], [124, -16], [-2, 26], [0, 0], [-210, 18], [148, 79], [0, 0], [-23, -23], [24, 88], [0, 0], [-139, 28], [275, 51], [0, 0], [-126, -66], [-16, 10], [0, 0], [-368, -172], [-86, 61], [0, 0], [630, 168], [20, -158], [0, 0], [-382, 49], [348, -30], [0, 0], [17, -122], [312, 144], [0, 0], [-494, 146], [-128, -101], [0, 0], [568, 148], [112, -286], [0, 0], [410, 56], [402, 101], [0, 0], [-458, -172], [-560, -134], [0, 0], [886, -59], [540, 204], [0, 0], [206, 24], [-740, -211], [0, 0], [352, 212], [-66, -192], [0, 0], [44, -117], [-372, 251], [0, 0], [468, 114], [-23, -46], [0, 0], [728, 112], [1064, 392], [0, 0], [-130, -456], [85, -111], [0, 0], [531, 70]]}