# Stored data for newform 99.4.a.a, downloaded from the LMFDB on 20 April 2024. {"label": "99.4.a.a", "space_label": "99.4.a", "level": 99, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67108963, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 463633063384591976, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, 1]]], "qexp_display": "q+q^{2}-7q^{4}+4q^{5}-26q^{7}-15q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1584, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 5.841189090568321, "hecke_ring_index": 1, "level_radical": 33, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [99, 1, [56, 46], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 11], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.968", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.948", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.899", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [11, 1]], "trace_display": [1, 0, 4, -26], "traces": [0, 1, 1, 0, -7, 4, 0, -26, -15, 0, 4, -11, 0, -32, -26, 0, 41, -74, 0, -60, -28, 0, -11, 182, 0, -109, -32, 0, 182, 90, 0, -8, 161, 0, -74, -104, 0, -66, -60, 0, -60, -422, 0, 408, 77, 0, 182, 506, 0, 333, -109, 0, 224, -348, 0, -44, 390, 0, 90, 200, 0, 132, -8, 0, -167, -128, 0, -1036, 518, 0, -104, -762, 0, -542, -66, 0, 420, 286, 0, -550, 164, 0, -422, 132, 0, -296, 408, 0, 165, -570, 0, 832, -1274, 0, 506, -240, 0, 14, 333, 0, 763, -1702, 0, -1132, 480, 0, -348, -564, 0, -320, -44, 0, -1066, 2142, 0, 728, -630, 0, 200, 1924, 0, 121, 132, 0, 56, -936, 0, -1606, -1455, 0, -128, 1908, 0, 1560, -1036, 0, 1110, 2186, 0, 2740, 728, 0, -762, 352, 0, 360, -542, 0, 462, 1310, 0, -1198, 900, 0, 286, -32, 0, 2114, -550, 0, 644, -4732, 0, 3868, 2954, 0, 132, -2004, 0, -1173, -296, 0, -2856, -678, 0, 2834, -451, 0, -570, 1680, 0, -4358, 832, 0, -2730, -264, 0, 814, -3542, 0, -240, 1778, 0, -3962, 14, 0, -2331, -374, 0, 2100, 1635, 0, -1702, -2340, 0, -1688, -1132, 0, -1312, 660, 0, 2232, 2436, 0, -564, 1632, 0, 208, -320, 0, 308, 2368, 0, 2128, -4186, 0, 2142, -2964, 0, -2550, 728, 0, -1350, 3042, 0, 2024, -1400, 0, 1924, -2700, 0, -578, 121, 0, -924, 1332, 0, 1920, 120, 0, -936, -3752, 0, -2002, -1606, 0, -119, -674, 0, 1716, 896, 0, 1908, 4352, 0, -1392, 1560, 0, 7252, -500, 0, -6538, -3034, 0, 2186, 1199, 0, 124, 2740, 0, 1560, -3642, 0, 4648, 5334, 0, 352, 10972, 0, 563, 360, 0, 3794, 3102, 0, 800, 990, 0, 1310, -5824, 0, -10608, -1198, 0, -2460, 528, 0, 1244, -2002, 0, -32, -2082, 0, 2378, 2114, 0, 3850, 496, 0, -990, -668, 0, -4732, 4440, 0, 3488, 3868, 0, 6330, -13156, 0, -2708, -924, 0, -2004, -4144, 0, 4034, -1173, 0, 2072, 88, 0, 260, -6120, 0, -678, -11084, 0, -3120, 2834, 0, -1771, 5622, 0, -3048, 3990, 0, 1680, 8500, 0, -3259, -4358, 0, -5824, -2168, 0, 7144, 7462, 0, -264, 9048, 0, -632, 814, 0, -7590, -2880, 0, -4220, 1680, 0, 1778, -8458, 0, 1144, -3962, 0, -98, -1740, 0, -13468, -4995, 0, -374, -2200, 0, -5126, 2100, 0, -4469, 3098, 0, 256, 11914, 0, -2340, 726, 0, 6390, -1688, 0, 7924, -5200, 0, 528, -5152, 0, 660, -9760, 0, -5138, 2232, 0, 5220, 8066, 0, -3432, 3948, 0, 1632, 7008, 0, 5578, 208, 0, 2240, -10920, 0, -10430, 660, 0, 2368, 4432, 0, -2280, 2128, 0, 4342, 6290, 0, 4642, -14994, 0, -2964, 3328, 0, 3054, -2550, 0, -5096, -12882, 0, 6148, 3690, 0, 3042, -5124, 0, 26936, 2024, 0, -3000, -4488, 0, 6540, -13468, 0, -2700, 16520, 0, 2112, -578, 0, -847, 56, 0, 524, -1980, 0, 1332, 15028, 0, -6660, 1920, 0, -328, 19812, 0, 9020, 6552, 0, -3752, 14812, 0, -6808, -2002, 0, 11242, -12660, 0, 14092, 11521, 0, -674, -4528, 0, -5566, 1716, 0, 1920, 3738, 0, -6352, -13356, 0, 4352, 592, 0, 20957, -1392, 0, -10920, 13504, 0, -2256, 15540, 0, -500, -3663, 0, -24728, -6538, 0, -11914, -1280, 0, -22756, -15302, 0, 1199, -5400, 0, 14300, 124, 0, -19180, 9526, 0, -13056, -4264, 0, -3642, -12068, 0, 8568, 4648, 0, 11430, -15090, 0, 4412, -2464, 0, 10972, -19838, 0, -3906, 563, 0, -2520, -3432, 0, 3828, 8130, 0, 3102, 12016, 0, 480, 800, 0, -2706, 11342, 0, 7696, -9170, 0, -5824, -20690, 0, -598, -10608, 0, 8386, 484, 0, -166, -9660, 0, 528, -16192, 0, 20108, 1244, 0, -4290, 2286, 0, -25660, 224, 0, -2082, 14820, 0, 9881, 2378, 0, -14798, 4884, 0, -11408, 8250, 0, 496, -6424, 0, -10656, -990, 0, -5820, 3378, 0, -11212, 33124, 0, 4440, 86, 0, -2200, 3488, 0, -27076, 4432, 0, 7632, -17302, 0, -13156, -4580, 0, 4282, -2708, 0, -1980, 6240, 0, 16380, 14028, 0, -4144, -1452, 0, 8438, 4034, 0, 8211, -34494, 0, -364, 4440, 0, 88, 13712, 0, 8744, 260, 0, 16728, 11136, 0, 11372, 4746, 0, -11084, 10960, 0, 31228, -3120, 0, -19838, 6398, 0, 3960, 1837, 0, 5622, 44252, 0, -5830, -3048, 0, 8550, -1456, 0, 1408, -11760, 0, 8500, -34530, 0, 29432, -3259, 0, 30506, -9810, 0, -17316, -12480, 0, -2168, -30192, 0, -27072, 7144, 0, 29302, 11396, 0, -17320, 1848, 0, 9048, -14588, 0, 5240, -632, 0, -5698, 14664, 0, 26152, 20746, 0, -2880, -4792, 0, -1066, -4220, 0, 3600, 37518, 0, 8320, -12446, 0, -8458, -6400, 0, -17290, 1144, 0, 27734, 17172, 0, 872, -210, 0, -1740, 25320, 0, 8382, -13468, 0, 13653, 8456, 0, -9536, 2618, 0, -2200, -55692, 0, -4224, -5126, 0, -14700, 20516, 0, -37444, -17549, 0, 3098, 5962, 0, -18928, 256, 0, 25530, -22470, 0, -3368, 16380, 0, 726, 15472, 0, -24480, 6390, 0, 11816, 10738, 0, -15912, 16980, 0, -5200, -22924, 0, -41690, 528, 0, 5344, -24642, 0, -8016, -4620, 0, -9760, 16450, 0, -16289, -5138, 0, -15624, -4692, 0, -3146, -14268, 0, 8066, -12012, 0, -30892, -3432, 0, 8460, 38906, 0, -1020, -11424, 0, 7008, -15078, 0, -2712, 5578, 0, -1456, 6050, 0, 33152, 4800, 0, -10920, 24336, 0, 22704, -10430, 0, -1804, 19358, 0, -11252, -16576, 0, 4432, -43684, 0, 41756, -2280, 0, -14896, -30360, 0, 6720, 37830, 0, 6290, -720, 0, 25752, 4642, 0, -32130, -17432, 0, 45804, 20748, 0, 3328, 15318, 0, -1452, 3054, 0, 17850, -49608, 0, 11350, -10920, 0, -12882, 24384, 0, 7194, 6148, 0, 14490, -33030, 0, -19980, -21294, 0, -5124, 3256, 0, -10006, 26936, 0, -14168, -2622, 0, -76804, 8200, 0, -4488, 39876, 0, 17344, 6540, 0, -28860, -38918, 0, 7112, 18900, 0, 16520, -56836, 0, -29727, 2112, 0, 4046, -15848, 0, 1114, -1815, 0, 56, 1688, 0, -71240, 524, 0, 5412, 41826, 0, 6270, -9324, 0, 15028, -978, 0, -1496, -6660, 0, -13440, 74256, 0, 47272, -1288, 0, 19812, 8400, 0, 51104, 9020, 0, 14040], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "33.4.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [1], [0], [-7], [4], [0], [-26], [-15], [0], [4], [-11], [0], [-32], [-26], [0], [41], [-74], [0], [-60], [-28], [0], [-11], [182], [0], [-109], [-32], [0], [182], [90], [0], [-8], [161], [0], [-74], [-104], [0], [-66], [-60], [0], [-60], [-422], [0], [408], [77], [0], [182], [506], [0], [333], [-109], [0], [224], [-348], [0], [-44], [390], [0], [90], [200], [0], [132], [-8], [0], [-167], [-128], [0], [-1036], [518], [0], [-104], [-762], [0], [-542], [-66], [0], [420], [286], [0], [-550], [164], [0], [-422], [132], [0], [-296], [408], [0], [165], [-570], [0], [832], [-1274], [0], [506], [-240], [0], [14], [333], [0], [763]]}