# Stored data for newform 37.3.d.a, downloaded from the LMFDB on 24 April 2024. {"label": "37.3.d.a", "space_label": "37.3.d", "level": 37, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 206208761893, "dim": 12, "is_polredabs": true, "trace_hash": 1614807625665250496, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-1+\\beta _{1}+\\beta _{6})q^{2}+\\beta _{5}q^{3}+(1-\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 37, "char_orbit_label": "d", "char_is_real": false, "Nk2": 333, "analytic_conductor": 1.0081769781330985, "hecke_ring_index": 2, "level_radical": 37, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.244", "prec": 17}, "analytic_rank_proved": true, "char_values": [37, 4, [2], [3]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 2, "level_primes": [37], "conrey_indexes": [6, 31], "field_disc": 6409170382666360658329600, "field_disc_factorization": [[2, 20], [5, 2], [494459753, 2]], "field_poly": [16, 312, 3042, -2054, 761, 704, 884, -268, 42, 8, 18, -6, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "11.542", "prec": 20}, {"__RealLiteral__": 0, "data": "1.515", "prec": 17}, {"__RealLiteral__": 0, "data": "563.716", "prec": 24}, {"__RealLiteral__": 0, "data": "403.415", "prec": 24}, {"__RealLiteral__": 0, "data": "44096.876", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "2.2.3.c4", "trace_display": [-6, 0, -6, -4], "traces": [0, 12, -6, 0, 0, -6, 6, -4, 36, -60, -16, 0, 64, 14, -70, -2, -96, 2, 132, 14, -24, 0, 22, 56, -84, 0, -48, 0, 0, 60, 0, 72, 208, 56, 112, -154, 0, -66, -336, -46, 0, 0, 90, 70, 80, 232, -424, -384, 0, 144, -34, -126, 328, -56, -194, 70, 16, -94, 0, 184, 276, 132, 0, -400, 0, 0, 614, 0, 116, 368, 556, 68, -692, 0, -382, 116, 12, 0, 0, -2, 4, -76, 374, 108, -1436, 0, 140, -420, -788, 278, -664, -450, 652, 584, 118, 0, 1584, -244, 416, 0, -856, 0, 0, 114, 0, -130, 130, 948, 668, -538, 0, -706, -208, -324, 0, 0, -8, -140, 544, 442, -624, -316, 0, 116, -752, -552, 856, 372, -600, 94, -244, -526, 0, 550, 812, 758, 0, 4, 0, 0, 336, 0, 170, 698, 1180, 308, -958, 0, -336, 0, -342, 0, 0, -664, 526, -284, 572, -1112, -1988, 0, 652, -392, -1362, -218, 128, -234, -306, 418, 540, 0, 540, -172, 808, 0, 168, 0, 0, 564, 0, 308, 360, 848, -980, 384, 0, -534, -1984, 442, 0, 0, 104, 392, -2100, 42, 1112, -464, 0, 336, 264, 200, 1568, 1284, 1234, 648, -1152, 178, 0, -968, 172, -462, 0, -1248, 0, 0, 1104, 0, 508, -52, -328, 1156, 628, 0, 998, 476, -1540, 0, 0, 88, 788, -1156, 92, -736, 500, 0, 908, 182, -1504, -458, -2552, -1420, -208, 1124, -396, 0, 4, -1172, -310, 0, 2748, 0, 0, -1774, 0, -32, -750, 392, 1224, -588, 0, -210, -1512, -692, 0, 0, -1172, -390, 2496, 1322, -356, 1396, 0, 296, 364, 2202, -1172, 1964, 784, -60, -1712, -768, 0, -1208, 846, -36, 0, 72, 0, 0, -644, 0, 444, 364, -1072, -904, 2872, 0, 1688, 2604, 178, 0, 0, -1034, -1080, -1336, -2668, 748, 1536, 0, 516, -442, -272, -514, -1580, 1178, -98, 676, 1400, 0, 254, -352, -2212, 0, -180, 0, 0, -258, 0, -1566, -328, -392, -1016, 340, 0, -1444, 364, 1012, 0, 0, 1870, -24, 288, 636, 1792, 1036, 0, -2976, 1290, 1212, -1612, 880, 1354, -1086, -80, -174, 0, -1346, 344, 950, 0, 1368, 0, 0, -910, 0, -140, 50, -6072, -240, -536, 0, 712, 872, 4024, 0, 0, 472, -1140, -160, -4002, 1724, 1808, 0, -660, 312, 4272, -1710, 2740, -956, -3540, 2804, 1428, 0, -2576, -2234, -782, 0, 136, 0, 0, -2246, 0, -1682, -5628, -24, -4300, 602, 0, 714, 2496, -268, 0, 0, 2588, 320, 5676, -1846, 3012, 4556, 0, -1780, 3032, 4186, 3254, 712, 680, 810, -4522, -1380, 0, -1678, -132, 530, 0, 300, 0, 0, 344, 0, 430, 888, -2396, -636, 2368, 0, 3124, 3488, -990, 0, 0, -1110, -2616, -1276, -632, -72, 3952, 0, -6056, 874, -1086, -3634, -3024, -342, -1058, 324, -348, 0, 852, -1004, -2652, 0, 884, 0, 0, -2662, 0, -198, -2264, -1064, 2672, -1788, 0, 442, -3204, 3856, 0, 0, 3968, -610, 4812, -306, 364, -260, 0, -2284, -2460, 2840, -5064, 3260, 4330, -1576, 312, 198, 0, -2870, 600, -294, 0, -496, 0, 0, 1852, 0, -2424, 1338, -4848, -624, 4144, 0, 3954, 3168, 952, 0, 0, -2994, 3344, -2612, -926, 1016, 4368, 0, 1844, 1212, 520, 250, -6648, -1304, 3768, 2288, -428, 0, -2124, -876, -3630, 0, -1264, 0, 0, -1032, 0, 1256, -1942, 2188, -4404, 1474, 0, -122, 4796, -1480, 0, 0, 1036, 162, -616, 378, -2284, 3636, 0, 3324, 3172, 1848, -1020, 2592, -196, 2304, -2602, 292, 0, -1046, 1374, -2366, 0, -28, 0, 0, -1088, 0, 4252, 546, -5356, 2128, -444, 0, -3128, -5064, -750, 0, 0, -2308, -2932, 672, 2708, -5560, -1412, 0, 3688, -3036, -818, -1214, 4128, -272, -1780, 1202, -248, 0, -146, 446, 2984, 0, 5332, 0, 0, -952, 0, -4542, 392, 280, -4180, -1538, 0, 826, -4200, -478, 0, 0, 2796, 154, -3500, 796, 4660, 344, 0, -2360, 6108, 412, 4500, -1572, -1264, 78, -1884, 2620, 0, 236, 2944, -2348, 0, -776, 0, 0, 578, 0, 1128, -22, -1388, 2504, 2756, 0, 1256, 4228, -2656, 0, 0, 4408, -928, -860, -558, 384, -3880, 0, 1284, 1648, -2508, -1220, -5300, -86, -2996, 324, -2134, 0, -1772, -2182, 3576, 0, -388, 0, 0, -2624, 0, 410, 1844, 9828, 3012, 100, 0, -2250, -8084, -1254, 0, 0, -6596, 182, 700, -1824, 384, -816, 0, 2648, -8148, 1672, 1094, 5924, 2472, 3114, 2862, -352, 0, 1308, 2008, 3038, 0, -1776, 0, 0, 8344, 0, -272, 2440, 1980, 2328, -1164, 0, 2168, 2976, -254, 0, 0, -2738, 6118, -9544, -2436, -2224, -7724, 0, 4256, -1826, -4272, 3724, 1924, -800, -1634, -4084, -408, 0, 7298, -1158, -2408, 0, -1136, 0, 0, 1120, 0, -532, 220, 520, 3280, -2368, 0, -6446, -2396, 1914, 0, 0, -104, 1620, 4480, 3890, 1400, -2928, 0, -8316, 432, -5392, 1400, -4080, -2566, -1738, -1076, 1172, 0, 670, -3204, 5436, 0, 1524, 0, 0, 352, 0, 6712, 1656, 5260, -372, -4996, 0, -790, -2876, -2168, 0, 0, -1524, -788, 1072, 3912, -168, -8772, 0, -3800, -2248, -10016, -516, 4276, -5208, 484, 6972, -148, 0, 5632, -796, 3034, 0, -1032, 0, 0, -1144, 0, 450, -1596, 4648, 3488, -2056, 0, 3388, 5076, 32, 0, 0, -3384, 2202, 3896, 1926, -528, 2416, 0, 10232, -4312, -266, 9246, -280, 4844, 2854, -2108, -2044, 0, 4444, -1124, -1452, 0, -4384, 0, 0, 1960, 0, -1148, 4308, 5536, 2032, -2354, 0, -12252, 292, -6204, 0, 0, -1942, -3546, -3244, 5956, -1708, -2392, 0, 7432, -850, -678, 3006, -4256, -1186, 3332, -4592, -1880, 0, 3464, 2506, 11044, 0, -2604, 0, 0, 1110, 0, -2502, 3000, 4556, -1036, -7150, 0, -3874, -6448, 1400, 0, 0, -308, -3332, -2676, -1510, -4084, -10416, 0, -3476, -8400, -2330, -1216, 1832, -4334, -128, 7424, 4358, 0, 4118, 1988, 3282, 0, -1816, 0, 0, 1348, 0, -6772, -3120, 11712, 216, -552, 0, -1616, -1820, 4168, 0, 0, 2152, 2444, 2444, 72, -1024, -13136, 0, 4616, 3754, -5596, 3916, -8668, -586, -68, 3440, 6744, 0, 4028, 770, -3000, 0, -1120, 0, 0, 4454, 0, 7004, 3710, 1332, 348, 1124, 0, 5150, 2672], "weight_parity": -1, "has_non_self_twist": 1, "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], [1, 1, 37, 4, -1, 4, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "37.3.d.a", "char_is_minimal": true, "conrey_index": 6, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, -1, 0, 1, 0, 0, -3, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], [2, 0, 0, 1, 1, -1, 1, 0, 0, -1, 0, -1], [0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, -1], [1, 0, 1, -3, 0, 0, 4, -1, 0, 1, 0, 0], [-5, 2, -1, 2, -1, 0, 0, 0, 0, 0, -1, 1], [-1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, -1, -3, -1, 1, 1, 0, 0], [3, -1, 3, -1, -3, 0, 0, 0, -1, 1, -2, 2], [0, 0, 1, -1, 0, 0, 1, -1, 0, -1, 0, 1], [-4, -2, -1, 0, -1, -1, 6, -1, -1, 0, -2, 0], [-2, 3, -1, 0, -2, -2, 2, -1, 0, 0, 0, 0], [-6, 5, -1, 5, 4, 0, 0, 0, 1, -1, 0, 0], [2, 0, 0, 0, -1, 1, 2, 0, 0, -1, 0, -4], [15, -11, 2, 0, 2, 2, -18, 2, 0, 0, 3, 0], [-1, 0, -1, -4, -1, 1, 3, 1, 0, 1, 0, 0], [-3, 0, -1, 0, -2, -2, 2, -1, -1, 0, 1, 0], [2, -2, 0, 2, 0, 4, -10, 5, 1, 1, 0, 0], [4, 0, -2, 2, 3, -3, 2, 2, 0, 0, 0, 1], [1, 0, 2, -5, 3, -3, 6, -2, 0, 0, 0, 3], [-13, 15, -3, 0, 5, 5, 10, -3, 2, 0, 3, 0], [-1, 0, 0, 0, 0, 1, -7, 3, -1, -1, 1, 1], [-5, 4, 1, 4, -3, 0, 0, 0, 1, -1, 1, -1], [1, 3, 0, -3, 0, -2, 21, 0, -2, -2, -4, -4], [5, -4, 0, 4, 0, 8, 6, 0, 0, 0, -1, -1], [9, -5, -1, 0, 2, 2, -8, -1, 0, 0, -1, 0], [2, -4, 0, 4, 0, 4, -23, 3, 1, 1, 2, 2], [6, -4, 1, 0, -3, -3, -7, 1, -1, 0, 1, 0], [20, -9, 3, 0, -8, -8, -16, 3, -1, 0, -4, 0], [5, 10, -2, 10, 0, 0, 0, 0, -1, 1, 0, 0], [7, 2, 2, 2, -6, 0, 0, 0, 1, -1, -3, 3], [-13, 0, 4, 4, 1, -1, -17, -4, 0, 1, 0, 2], [-15, 16, 0, -16, 0, -3, 60, -7, 0, 0, -1, -1], [-11, 0, 4, -7, 2, 6, -7, 3, -1, 1, 1, 1], [-24, 1, -6, 1, 6, 0, 0, 0, 0, 0, 1, -1], [-1, -8, -4, 0, -1, -1, -4, -4, 2, 0, 5, 0], [2, 1, 0, -1, 0, 3, -5, -2, 1, 1, -3, -3], [6, -7, 0, 7, 0, -3, 10, -2, 1, 1, 1, 1], [0, 0, 0, -24, 8, -8, 24, 0, 0, 1, 0, -4], [5, 0, 4, 2, 3, -3, 3, -4, 0, 3, 0, 2], [4, -9, -2, -9, -9, 0, 0, 0, -1, 1, -2, 2], [19, 0, -1, -5, 4, -4, 24, 1, 0, -3, 0, 0], [-35, 11, -5, 11, -3, 0, 0, 0, -1, 1, 0, 0], [-32, -2, 3, -2, 2, 0, 0, 0, 1, -1, 0, 0], [25, -25, 0, 25, 0, -9, -80, 7, -4, -4, 0, 0], [12, 5, -3, 5, -6, 0, 0, 0, 3, -3, 6, -6], [-13, 0, 2, -20, -2, 2, 7, -2, 0, 2, 0, -3], [0, -20, 3, 0, 4, 4, 0, 3, 1, 0, 0, 0], [23, 1, 2, 0, -2, -2, -28, 2, 0, 0, 5, 0], [-3, 2, 1, 2, 8, 0, 0, 0, -2, 2, 1, -1], [-19, 0, 1, 15, -14, 14, -34, -1, 0, 2, 0, 10], [12, 3, -2, 0, 1, 1, 1, -2, 1, 0, -13, 0], [5, 0, 0, 6, 3, -3, -1, 0, 0, -4, 0, 2], [-16, 20, 2, 0, 3, 3, 18, 2, 3, 0, -2, 0], [-1, 2, 0, -2, 0, -3, 46, -5, -3, -3, -1, -1], [25, 0, -5, 14, 2, -2, 11, 5, 0, -2, 0, 0], [20, 0, -2, -17, 2, -2, 37, 2, 0, -1, 0, -8], [9, 8, 1, 0, 0, 0, -2, 1, -7, 0, -7, 0], [-17, 15, 0, -15, 0, 9, 27, -6, 4, 4, 2, 2], [-39, 9, 2, 9, -12, 0, 0, 0, -3, 3, -4, 4], [-29, 17, 0, -17, 0, 8, 21, -7, 7, 7, 12, 12], [-1, -1, 0, 1, 0, 6, 15, 9, 0, 0, 2, 2], [55, -11, 8, 0, 4, 4, -55, 8, -2, 0, 0, 0], [13, -9, 0, 9, 0, -9, -9, -4, -3, -3, -4, -4], [7, 14, 4, 0, 9, 9, -3, 4, 4, 0, -4, 0], [27, 2, -6, 0, 6, 6, -42, -6, 5, 0, 15, 0], [48, -1, 2, -1, 4, 0, 0, 0, 3, -3, 1, -1], [3, 3, -7, 3, -10, 0, 0, 0, -5, 5, 6, -6], [-29, 0, -8, 41, 4, -4, -70, 8, 0, -4, 0, -7], [-5, 6, 0, -6, 0, -3, 55, 11, 1, 1, -1, -1], [-33, 13, -9, -13, 9, -5, 11, -2, 2, -3, -2, -8], [4, -7, 6, -7, -12, 0, 0, 0, 1, -1, -2, 2], [20, -38, 5, 0, -3, -3, -12, 5, -8, 0, -8, 0], [-1, -8, 0, 8, 0, 2, -18, -5, -3, -3, 9, 9], [17, -13, 0, 13, 0, -11, 41, -4, -3, -3, -4, -4], [-16, 0, -1, -29, -5, 5, 13, 1, 0, -3, 0, 1], [6, 0, -7, 8, -4, 4, -2, 7, 0, -1, 0, -1], [1, -19, 1, -19, 18, 0, 0, 0, 5, -5, 0, 0], [38, 0, 5, 17, 2, -2, 21, -5, 0, 1, 0, 1], [7, -11, 15, -11, 6, 0, 0, 0, 3, -3, 8, -8], [-119, 9, -6, 9, 0, 0, 0, 0, -4, 4, -12, 12], [2, 1, 0, -1, 0, -6, -64, -10, 4, 4, -3, -3], [16, 19, -4, 19, 8, 0, 0, 0, 1, -1, -1, 1], [-41, 0, -4, 0, -9, 9, -41, 4, 0, 5, 0, 7], [-74, 6, -3, 0, 3, 3, 57, -3, 7, 0, 17, 0], [22, 18, -1, 0, -6, -6, -2, -1, -3, 0, -20, 0], [-64, 13, 1, 13, -20, 0, 0, 0, -5, 5, -4, 4], [-46, 0, 4, -18, 14, -14, -28, -4, 0, 5, 0, 4], [65, -41, 1, 0, -5, -5, -80, 1, -2, 0, 15, 0], [33, 0, 5, -25, -6, 6, 58, -5, 0, 3, 0, -2], [20, -22, 0, 0, -6, -6, -18, 0, 1, 0, -2, 0], [-3, -1, 0, 1, 0, -4, 2, -8, -1, -1, 4, 4], [91, 0, 21, -65, -5, 5, 156, -21, 0, 8, 0, -3], [-8, 0, -9, 18, -1, 1, -26, 9, 0, 2, 0, -2], [30, 1, 11, 0, -12, -12, -24, 11, 3, 0, -6, 0], [12, 2, 0, -2, 0, -12, 3, -3, -2, -2, -14, -14], [-63, 19, -12, 19, 13, 0, 0, 0, 0, 0, 3, -3]]}