# Stored data for newform 43.4.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "43.4.a.a", "space_label": "43.4.a", "level": 43, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67108907, "dim": 4, "is_polredabs": true, "nf_label": "4.4.45868.1", "trace_hash": 992441136467076638, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [2, -14, -9, 4, 1]]], "qexp_display": "q+(-1+\\beta _{3})q^{2}+(-3+\\beta _{2}-\\beta _{3})q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 688, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 2.5370821302468465, "hecke_ring_index": 1, "level_radical": 43, "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": [43, 1, [3], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [43], "conrey_indexes": [1], "field_disc": 45868, "field_disc_factorization": [[2, 2], [11467, 1]], "field_poly": [1, 11, -10, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.746", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "37.596", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "563.176", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[43, -1]], "trace_display": [-4, -11, -27, -20], "traces": [0, 4, -4, -11, 2, -27, -27, -20, -66, -9, -3, -62, 61, -2, 112, 92, 202, -207, 299, 99, 81, -90, 202, -103, 209, -101, -50, -218, -80, -99, 300, 131, -342, -32, 53, -374, -379, -449, -609, 98, 133, -491, -394, 172, -764, -338, 1061, 19, 237, 236, 599, 1649, 224, -1220, -322, 1360, 344, 232, -771, 816, -156, 372, -97, 1914, 434, -350, 812, 110, -1697, -1238, -718, 468, -315, 628, 395, 62, 1671, -2044, -90, 1095, -31, 2056, -2287, -980, -610, -152, -172, -507, 1816, -738, -2398, 852, -2517, -35, -2233, 1149, -1551, -1765, 1652, -58, -2123, -3696, 3193, -2253, -76, 2812, 1956, 780, -890, 250, -388, 1835, -4616, -1510, 696, 707, 8541, -72, -632, 1566, -3124, 3014, 1968, 4238, 437, 1260, 1142, -1115, 1922, -473, 262, 2927, 824, -4978, -1530, 4773, 11799, 1386, -1306, -3430, 1978, 383, 1604, -2710, -7483, 1050, 1400, -3903, -1881, -2231, -502, -1212, -5341, -7031, -4144, -5674, -758, -2129, 4203, 3878, 1757, 2098, -2200, -4807, 9107, -3084, -6572, -1062, 5254, -7754, 5604, -5914, 86, -8294, -3735, 6502, -2308, -2658, 7962, 4917, 474, 5110, 624, -3706, 3491, 3786, -3011, -3874, 15243, -10048, 1857, 5966, -2875, 1475, -4961, 292, -6214, -4252, -10818, 4358, 7989, 4674, 8184, 6654, -8359, 10383, -4545, 10954, -440, 3656, 5948, 411, -8690, 338, -8468, -1161, 7606, 10658, 7570, -106, -6028, 3460, 5191, -2720, 5176, 4722, -646, 11805, 2760, -8506, -5853, 12600, -23631, 1158, 1776, -1038, -1440, -13134, -14118, -5979, -5500, 5734, -3130, -722, -8980, 5153, 9282, -2074, 477, 10108, -116, -9044, 670, 10670, 10657, -17337, -6350, -13548, -1161, -1918, 1974, 11439, -7973, -8020, -5512, 11576, 4318, -6774, -2244, -1942, 6745, -6115, -12385, -3644, 2986, -8594, 2370, 7475, -3870, 4277, 5170, -2475, -5333, -10552, -16048, -6487, 1898, -14982, 18633, 33985, -7374, 13222, -19116, -610, -1823, -286, 13219, 20996, 15317, -3564, -4954, -860, -2344, 8402, 21007, -2346, -28043, 19220, 26304, 12390, 370, -14202, 434, 14098, 4731, -14360, -7825, -6910, 13994, -15024, -8935, 6238, -4602, -14428, 8030, 4136, 17249, -18040, -11485, 10922, -9396, -3772, 28670, -5999, 13354, -7394, 13054, 9539, 8374, 8892, 12196, -30150, 6262, -8104, -2838, 12441, 16082, 9951, 1917, -4479, -6166, -5928, 18956, -8478, -2778, -14522, -20742, 18050, -3619, -7077, 22722, -7165, 9070, -1343, -8672, -5154, -4210, -3635, -23285, -26590, 4010, -8336, -5387, -379, -3570, -6773, -38633, 4578, -16736, 2764, -9179, -7545, -6546, -4956, -583, 5144, -3905, -387, 24197, -10356, 1132, -16132, -938, 2809, 3628, -7725, 20680, -8250, -21690, 18044, -24203, 10265, 5966, 10604, -31718, -23130, 28254, 13808, -24603, -1062, 10791, -15606, 27753, -17208, -10046, 18562, -5160, 24076, 22408, 25244, -8356, -18761, 16599, 7453, 41226, 29936, -334, -2488, 25684, 5376, -129, -10255, 11670, 11276, 7878, 23889, -5348, -12047, 5422, 781, 1180, 11955, 324, -4670, -7605, -13596, -1580, -13855, 22344, 20364, -7838, 18666, 6746, -1706, -14095, 780, -16160, 24764, -19714, 20367, -3945, -24638, 12464, 1510, 10701, 13897, -32266, 21339, -3718, 3908, -5086, -9552, -12720, -2666, -23854, -27057, 9490, -11488, 14161, 24453, 16444, -1850, -8442, -11904, -21798, 9333, -14598, 21099, 9644, -556, -11159, 13239, -4874, -59457, -3346, -2216, -11211, 11792, 16680, 7555, 6628, -1268, 7324, 2556, -52338, 31680, -39618, 21707, -40949, 4736, -35677, -16648, 5298, 23115, -8352, 22377, 2623, -42256, -21190, 8844, -2794, -13362, 48687, -14205, 13015, -20640, -16660, 30821, -29056, -8159, 7620, -7258, -3514, -4320, -14550, 12542, 23256, 8404, 23154, 55522, -16347, -17462, 12681, -38368, -9317, -1136, -1364, -20786, -4474, 14798, -21482, 8922, 25058, 11182, -25741, -23709, 18364, 5654, 26993, -86, 7242, -21364, -57519, -10562, -753, -7534, 43648, 18880, 46424, -5018, -14339, -12489, 13528, -5468, -1642, 4743, 27621, -23442, -11427, 21770, -23886, -21368, 17362, 55442, 46372, 5364, 9670, 36556, 21097, -30626, -742, 3894, -18369, 13534, 7644, 38244, -29823, -3948, 6964, 36883, 16006, -6954, 4816, -32300, 28640, -10387, 36118, 16392, -29405, -61734, -8522, 13486, 83719, 6234, -30764, -51335, -12024, 51213, 20442, -6800, 30330, -6409, 67414, 54732, 8450, -9270, -20562, -31692, 15987, 40217, -35016, -8720, -27101, -18891, -17198, 14278, -16210, -22674, 23964, -8034, -27739, -53248, 11254, -10872, 42462, 3956, 76044, -38838, -50286, 21544, 2704, -52910, -51471, -65185, -32524, -41124, 52163, -25562, 49394, 68498, 8572, -57422, 50232, -4082, -44310, 12006, -51091, -6492, -66260, 42350, 22826, 22424, -16906, 1338, -20889, -29991, -11154, 12341, 6844, 13622, -86380, -22064, 7370, -12114, -40950, 16112, -45056, 33682, 8686, -11634, 22421, -27484, -15442, -21892, -36329, -8276, 14265, -5764, 62105, 21672, -2414, -25476, 272, -5286, -59756, 27975, 67666, -13368, 20526, 61562, 12518, 74596, 48810, -25362, 55570, 10196, -73791, -30714, 2535, -18159, 41506, -906, -21953, -39704, -18942, -23340, 6821, -50546, 2344, -27945, 15710, -8901, 12382, 14717, -41711, 14828, 71583, -43562, -30534, 12559, -7622, 9020, -65828, 75258, 31137, -6798, 18593, -56594, 148320, -49040, -24305, -54788, 36435, 9870, -1626, 44026, 63344, 51131, -5788, 24804, 249, -41502, 5639, 30196, -29514, 147391, 36116, -13160, 11741, 31421, 19896, 51408, -53507, -32643, 12857, 54470, -9723, 40534, 37012, 65109, -1236, -35180, -86844, -73203, 674, 44633, -14883, 27072, 37288, 62278, -44009, 45924, 9516, -10368, 21494, -61042, 89794, -52602, 30508, -64027, 20929, 86946, -2579, 27728, -21174, -28102, -3412, -26342, 130614, -39813, -10830, -95811, -135162, 26914, -20472, 29903, -31495, 4257, -113410, -6680, -55301, 79202, -16102, -13006, -23727, 34828, 13784, -53924, 41916, -39563, 24022, 4468, 17504, -97851, 26664, -28372, -123884, -84707, -30448, 92722, -65316, 134491, -23717, 106685, -87073, 57079, 91937, -68864, -61594, -40870, -93856, 6792, -14270, 28532, -8512, 28203, -63356, -73175, 4500, -28625, 3483, 89096, 4357, -67834, -4122, 44214, -102616, -123505, -74834, 22132, 37293, 18062, -43632, -44022, 58221, 37300, 2142, 56480, 23865, -13774, 26220, 45851, -18425, 88170, -43994, 4788, 18994, 90000, -42049, -14514, -34380, -97730, -51108, 16242, -24587, -30329, 15416, -112, -86000, 23679, 58924, 94272, 71114, -3870, 29458, -63122, 7478, 194, 7557, -6228, -1348, 8410, -25016, -2982, 344, 24608, 154100, 22458, 71003, -3915, 45963, -61468, 25802, 13604, -59520, 7280, -74270, -37098, -22815, 49424, 40733, 34183, 104370, -37704, 48375, 27304, -2522, 81186, -19208, -4626, -21710, 43116, -4736, -51963, 56752, 65634, 8686, 18246, 43090, -10616, 63011, 79072, -6318, -73352, -155864, -28466, 92909, 100812, -60847, -48068, 69524, 7453, 5030, -79386, 113926, -26199, -48536, 42561, 27746, -51051, 28253, -29284, 46006, 76452, -87593, -11856, -23852, -79071, 22604, -25020, -35059, 135550, -44633, -33354, -126234, -5622, 145455, -96386, 32466, -4429, 82756, -104944, -37095, -28968, -36648, 16714, -16220, -17347, 11779, 63167, -39524], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "43.4.a.a", "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, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 0, 1], [-3, 0, 1, -1], [1, 1, -3, -4], [-6, -3, 0, -1], [-7, -2, 3, -1], [-6, 8, -4, 2], [-19, -1, 11, 8], [-1, 5, -10, 7], [-2, -1, 6, -3], [-12, -19, 5, 6], [17, -4, -3, 1], [-2, 7, -1, -2], [30, 6, -14, -8], [25, 11, -19, 8], [53, -11, 1, -22], [-65, 15, 38, 5], [77, 17, -26, -12], [30, -21, 0, -17], [14, 15, 10, 9], [-22, -40, 38, -6], [50, 1, 1, -35], [-20, -12, -11, 29], [53, 20, -23, 25], [-36, 34, 9, 19], [-12, -1, -1, 5], [-51, -59, 45, -6], [-18, -58, 50, 52], [-9, 42, -105, -57], [77, 27, -35, 20], [15, 79, -8, -1], [-79, -15, -11, 54], [-8, 60, -60, 10], [29, -33, -30, -118], [-96, -14, 24, -30], [-113, -26, 99, 83], [-115, -22, 33, 7], [-166, -17, 72, 81], [26, -20, 14, 4], [54, 7, -90, 1], [-104, -66, -9, -95], [-102, -44, 58, -42], [43, 0, 0, 0], [-236, 116, 64, 106], [-115, -25, 147, -52], [274, 40, -75, -96], [17, 98, -147, -113], [57, 80, -71, -7], [93, -140, 4, 64], [170, 10, -91, -102], [426, 59, -114, 131], [70, -50, -6, -10], [-306, -99, 103, 52], [-87, -51, 77, -78], [304, 78, 66, 50], [94, -46, 14, -160], [59, 97, -101, 4], [-237, 48, 129, 267], [222, -94, 22, 12], [-47, -33, 65, -12], [98, -50, 30, 86], [-7, 7, -76, 26], [514, 30, -172, 56], [109, 153, -155, -54], [-76, -12, -34, -12], [208, 70, -90, 22], [-26, 89, 125, -14], [-393, -208, 83, 373], [-319, -55, 93, -60], [-192, -54, 104, -30], [50, 92, 176, 116], [-37, -152, -15, -365], [122, -94, 234, 130], [105, -26, 1, -169], [15, -113, 115, 16], [430, 177, -226, -345], [-548, 282, -134, -242], [-22, -10, 8, 0], [320, -29, -156, 135], [22, -29, -90, 69], [496, 189, -117, -36], [-638, -86, 351, 190], [-212, -41, -91, -276], [-174, 220, -134, 14], [87, 39, -539, 38], [-43, 0, 0, 43], [-96, -327, 204, -87], [556, 34, -442, -338], [-222, 198, -48, 228], [-595, -199, 181, -106], [232, -154, 78, 70], [-732, 75, 336, 405], [-12, -259, 272, -29], [-627, 34, 241, 503], [271, 62, 3, 101], [-395, -96, 125, -51], [-468, 170, -63, -241], [411, 60, -52, -103], [-112, 133, 257, -294], [-516, -283, 224, 415]]}