# Stored data for newform 810.4.e.i, downloaded from the LMFDB on 13 December 2024. {"Nk2": 12960, "analytic_conductor": 47.7915471046499, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [810, 3, [731, 487], [1, 3]], "cm_discs": [], "conrey_index": 271, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[7, [16, -4, 1]], [11, [2304, -48, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36029071963980586, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "810.4.e.i", "level": 810, "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": [2, 3, 5], "level_radical": 30, "minimal_twist": "30.4.a.b", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+(-2+2\\zeta_{6})q^{2}-4\\zeta_{6}q^{4}+5\\zeta_{6}q^{5}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "810.4.e", "trace_display": [-2, 0, 5, 4], "trace_hash": 579148389404881707, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.008", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.257", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "115.666", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, -2, 0, -4, 5, 0, 4, 16, 0, -20, 48, 0, -2, 8, 0, -16, -228, 0, 280, 20, 0, 96, -72, 0, -25, 8, 0, -32, -210, 0, -272, -32, 0, 228, 40, 0, -668, -280, 0, 40, 198, 0, 268, -384, 0, 288, -216, 0, 327, -50, 0, -8, -156, 0, 480, 32, 0, -420, -240, 0, -302, 1088, 0, 128, 10, 0, -596, 456, 0, -40, -1536, 0, -956, 668, 0, -560, -192, 0, 640, -160, 0, -792, 348, 0, -570, 536, 0, 384, 420, 0, -16, -288, 0, -432, 700, 0, 1534, -1308, 0, 200, -1722, 0, -1052, -16, 0, 156, -1128, 0, -1220, -480, 0, 64, -1302, 0, 360, 1680, 0, 960, -456, 0, -973, -604, 0, -1088, -250, 0, -248, -128, 0, 20, -192, 0, 560, 2384, 0, -1824, 2514, 0, -1340, -80, 0, 1536, -192, 0, -2100, 956, 0, 1336, -1410, 0, 2128, 2240, 0, 768, 1360, 0, -3026, 1280, 0, 160, -576, 0, 5224, 792, 0, 696, 24, 0, 2193, 2280, 0, -2144, -1962, 0, 100, 768, 0, -420, -240, 0, 1804, 16, 0, -576, -1670, 0, -5472, 1728, 0, -2800, 168, 0, 1318, 3068, 0, 1308, -8028, 0, 4000, -200, 0, -3444, 840, 0, -990, 4208, 0, 64, 6720, 0, 3868, 312, 0, 1128, 2680, 0, -2176, 1220, 0, -960, 228, 0, 3148, -256, 0, 5208, -2556, 0, 610, 720, 0, -1680, -4116, 0, -2160, -960, 0, -912, -4920, 0, 1438, 3892, 0, 2416, -1635, 0, -280, -2176, 0, 250, 1584, 0, -6912, 248, 0, -256, -2166, 0, -1336, -80, 0, 768, -3192, 0, -390, 1120, 0, -2384, 10980, 0, -12656, 1824, 0, 5028, 1200, 0, 574, 5360, 0, 320, -4242, 0, 628, 3072, 0, 192, 1584, 0, 16166, 2100, 0, 1912, 558, 0, 1200, -5344, 0, 5640, -144, 0, -1072, 4256, 0, -2240, -3020, 0, -13928, -768, 0, 2720, -2832, 0, -8642, 12104, 0, -5120, 2214, 0, 10080, 320, 0, 576, -31920, 0, 100, -5224, 0, 1584, 864, 0, -10772, -2784, 0, -96, 2980, 0, 1654, 4386, 0, -2280, -26112, 0, 5360, 2144, 0, -3924, -2196, 0, -8270, -400, 0, -3072, -10302, 0, -3840, -840, 0, 240, -4560, 0, 25482, -1804, 0, 32, -2390, 0, 8764, 2304, 0, 6680, -312, 0, 1318, -10944, 0, -1728, 840, 0, 2200, 2800, 0, 336, 3528, 0, 960, -5272, 0, -12272, 9630, 0, 8208, 2616, 0, 8028, 6400, 0, -6188, -4000, 0, -400, 1638, 0, -544, 13776, 0, -3360, -16032, 0, 13750, -1980, 0, -4208, -1920, 0, 3480, -64, 0, 13440, 12480, 0, -7262, -15472, 0, -1248, 2850, 0, 1208, 2256, 0, -2680, 19584, 0, 3604, 2176, 0, 2440, -10080, 0, 2320, 3840, 0, -912, -11172, 0, 1050, 6296, 0, 256, 13620, 0, 19008, -5208, 0, -5112, -40, 0, -17066, -2440, 0, -2880, 18918, 0, -1052, -3360, 0, 4116, 22152, 0, -4768, 2160, 0, -1920, -12864, 0, -3500, 3648, 0, 19680, 9000, 0, 668, 2876, 0, -3892, 15340, 0, -17528, -2416, 0, -3270, -5592, 0, 23940, 1120, 0, 8704, -3072, 0, -4700, 500, 0, -1584, -23616, 0, -17220, 6912, 0, 496, -1170, 0, -1912, 1024, 0, 8664, 5260, 0, 10368, -2672, 0, 80, -33276, 0, 31384, -768, 0, -6384, 31008, 0, 6983, 1560, 0, -4480, 396, 0, -2820, -4768, 0, -10980, 31392, 0, -44036, 12656, 0, 3648, -3050, 0, 4564, -20112, 0, -4800, -29400, 0, -2560, 1148, 0, -5360, -15468, 0, -1072, -320, 0, -8484, 20148, 0, 6510, -2512, 0, -12288, 24030, 0, -2372, 384, 0, -1584, 3600, 0, 17092, -16166, 0, 4200, -1392, 0, -3744, -7648, 0, -2232, 15444, 0, -38080, 2400, 0, 5344, 36684, 0, -4560, -5640, 0, -288, -24600, 0, 8998, 4288, 0, -17024, 4865, 0, -4076, -4480, 0, 3020, 864, 0, -8156, 13928, 0, -1536, -10086, 0, -8780, -10880, 0, 11328, 840, 0, -625, -17284, 0, -12104, 76152, 0, 5584, 5120, 0, 4428, -620, 0, 654, -40320, 0, -1280, -7602, 0, -24212, 1152, 0, 31920, 18912, 0, -23040, -100, 0, -10448, 9558, 0, 960, -6336, 0, -3456, 29280, 0, 29098, -21544, 0, 2784, 5600, 0, 30240, 96, 0, 5960, 14496, 0, 11638, -6616, 0, -17544, -3426, 0, -6136, -4560, 0, 26112, -40296, 0, 25140, -5360, 0, 4288, 156, 0, 29428, 15696, 0, 8784, 6700, 0, -22572, -16540, 0, 400, 32484, 0, -93520, 3072, 0, -20604, 6888, 0, -2030, 15360, 0, 3360, -19584, 0, -480, 480, 0, 4560, 13920, 0, -8416, -25482, 0, -3608, -5250, 0, -18596, -128, 0, 9560, -30552, 0, -21242, 17528, 0, -2304, -57216, 0, -680, -6680, 0, -624, 21888, 0, 7050, -5272, 0, 43776, -2256, 0, -17792, -3456, 0, -840, 21280, 0, 74692, -2200, 0, 5600, 11358, 0, -2440, -1344, 0, -14112, -480, 0, 34270, 1920, 0, 5272, -26556, 0, 13600, 12272, 0, 19260, 27720, 0, -36864, -32832, 0, -10464, 15130, 0, 11164, 16056, 0, -6400, -10416, 0, 1208, 6188, 0, -8000, 5094, 0, 24624, 1600, 0, -6552, -22944, 0, -1440, -1088, 0, -13776, -17580, 0, 11704, 3360, 0, -32064, 13060, 0, 37520, -55000, 0, 7920, 29478, 0, -39332, -8416, 0, 1920, 13512, 0, 7900, -3480, 0, -128, -37278, 0, -120, -53760, 0, -49920, -12360, 0, -19711, -14524, 0, 15472, 21930, 0, -7784, 1248, 0, 5700, 24048, 0, 35998, -4832, 0, -9024, 21594, 0, -9260, -5360, 0, -19584, 63264, 0, -19620, -3604, 0, 4352, -30720, 0, -1192, -9760, 0, 40320, -500, 0, 39694, 4640, 0, -3840, 2484, 0, -5336, 912, 0, -22344, 4344, 0, -496, -4200, 0, -25184, -30240, 0, -600, 512, 0, -13620, 114240, 0, 17784, -19008, 0, -10416, 4510, 0, -4436, 20448, 0, 160, -22752, 0, -16704, -34132, 0, 2440, -1536, 0, -54320, 2880, 0, 37836, 1536, 0, 8350, 4208, 0, 13440, 33030, 0, 45780, 8232, 0, -22152, -54720, 0, -59948, 4768, 0, 4320, -13962, 0, 14256, 7680, 0, 51456, -35196, 0, 956, -7000, 0, -3648, -56676, 0, 1680, -19680, 0, 18000, -10056, 0, -44193, -2672, 0, -11504, -6590, 0, 17524, -7784, 0, -15340, -53616, 0, -10720, 17528, 0, -4832, 10914, 0, 10080, 13080, 0, 22368, -22272, 0, -20070, 47880, 0, -1120, -38592, 0, 28144, -8704, 0, -6144, 10000, 0, -4826, 18800, 0, -2000], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [-2, 2], [0, 0], [0, -4], [0, 5], [0, 0], [4, -4], [8, 0], [0, 0], [-10, 0], [48, -48], [0, 0], [0, -2], [0, 8], [0, 0], [-16, 16], [-114, 0], [0, 0], [140, 0], [20, -20], [0, 0], [0, 96], [0, -72], [0, 0], [-25, 25], [4, 0], [0, 0], [-16, 0], [-210, 210], [0, 0], [0, -272], [0, -32], [0, 0], [228, -228], [20, 0], [0, 0], [-334, 0], [-280, 280], [0, 0], [0, 40], [0, 198], [0, 0], [268, -268], [-192, 0], [0, 0], [144, 0], [-216, 216], [0, 0], [0, 327], [0, -50], [0, 0], [-8, 8], [-78, 0], [0, 0], [240, 0], [32, -32], [0, 0], [0, -420], [0, -240], [0, 0], [-302, 302], [544, 0], [0, 0], [64, 0], [10, -10], [0, 0], [0, -596], [0, 456], [0, 0], [-40, 40], [-768, 0], [0, 0], [-478, 0], [668, -668], [0, 0], [0, -560], [0, -192], [0, 0], [640, -640], [-80, 0], [0, 0], [-396, 0], [348, -348], [0, 0], [0, -570], [0, 536], [0, 0], [384, -384], [210, 0], [0, 0], [-8, 0], [-288, 288], [0, 0], [0, -432], [0, 700], [0, 0], [1534, -1534], [-654, 0], [0, 0], [100, 0]]}