# Stored data for newform 38.4.a.c, downloaded from the LMFDB on 27 March 2023.
{"level_primes": [2, 19], "is_polredabs": true, "sato_tate_group": "3.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 6356589279097825, "level_radical": 38, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 3, "analytic_conductor": 2.242072580218143, "inner_twist_count": 1, "field_disc_factorization": [[73, 1]], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "38.4.a.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "38.4.a.c", "field_poly_is_cyclotomic": false, "dim": 2, "trace_zratio": 0, "traces": [0, 2, 4, 9, 8, -9, 18, -18, 16, 23, -18, -17, 36, 17, -36, -150, 32, -80, 46, 38, -36, -227, -34, 73, 72, 119, 34, 189, -72, 3, -300, 212, 64, -40, -160, 519, 92, 192, 76, 551, -72, -50, -454, 677, -68, -1089, 146, -389, 144, 60, 238, -433, 68, -1219, 378, -33, -144, 171, 6, -287, -600, 313, 424, -1521, 128, -1500, -80, 1223, -320, 803, 1038, 200, 184, 378, 384, 1521, 152, 7, 1102, 1350, -144, 1142, -100, -670, -908, 579, 1354, -753, -136, -236, -2178, -2051, 292, -652, -778, -171, 288, 1294, 120, 133, 476, -2416, -866, -1420, 136, 3978, -2438, 167, 756, -1121, -66, -158, -288, 784, 342, -1752, 12, 4466, -574, 1012, -1200, -2481, 626, 140, 848, -2367, -3042, 3000, 256, 3302, -3000, -1485, -160, -342, 2446, -3588, -640, 3828, 1606, -3131, 2076, -4342, 400, 330, 368, 2286, 756, 2898, 768, 2153, 3042, 1860, 304, -1577, 14, 3864, 2204, 248, 2700, -4865, -288, -2555, 2284, -4376, -200, 618, -1340, 402, -1816, 1919, 1158, 437, 2708, -804, -1506, -5013, -272, -379, -472, 262, -4356, -7156, -4102, 5460, 584, 2202, -1304, 607, -1556, -5351, -342, 1054, 576, 3262, 2588, -9816, 240, 2050, 266, 454, 952, 2693, -4832, 3039, -1732, -870, -2840, 5110, 272, -323, 7956, -1935, -4876, 5134, 334, -3813, 1512, 4516, -2242, -5015, -132, -1629, -316, 6524, -576, 10238, 1568, 2183, 684, -6981, -3504, 944, 24, 3021, 8932, 9525, -1148, 3958, 2024, 7650, -2400, -1518, -4962, -1278, 1252, -8154, 280, 323, 1696, 4066, -4734, -903, -6084, -146, 6000, 7314, 512, -11628, 6604, 2360, -6000, -6864, -2970, 4551, -320, 3624, -684, -7924, 4892, -10234, -7176, -2975, -1280, -14741, 7656, -26, 3212, 3537, -6262, -12016, 4152, 2134, -8684, 831, 800, -2850, 660, -1010, 736, -6480, 4572, 9546, 1512, -2041, 5796, -1446, 1536, -694, 4306, 6789, 6084, -7115, 3720, -6638, 608, -13563, -3154, 1724, 28, -550, 7728, 13348, 4408, 8483, 496, 20751, 5400, -4995, -9730, -792, -576, -6293, -5110, -1520, 4568, 13823, -8752, -17199, -400, 13867, 1236, 5813, -2680, -6990, 804, 2928, -3632, 14620, 3838, -5962, 2316, -3408, 874, -4878, 5416, -14016, -1608, 11173, -3012, 4971, -10026, 13469, -544, 16875, -758, -13602, -944, 11051, 524, -13344, -8712, 722, -14312, -11785, -8204, 18447, 10920, 1084, 1168, 2710, 4404, 8489, -2608, 1435, 1214, -7914, -3112, -9939, -10702, -7235, -684, 22990, 2108, 2822, 1152, -2769, 6524, 10085, 5176, -3163, -19632, -3869, 480, -10734, 4100, 276, 532, -2047, 908, -4313, 1904, 3144, 5386, -19076, -9664, -1197, 6078, -2654, -3464, -9856, -1740, 10875, -5680, -1067, 10220, -18228, 544, -3030, -646, -7104, 15912, 12285, -3870, -27797, -9752, -6731, 10268, -19023, 668, -2238, -7626, 4850, 3024, -4984, 9032, 13572, -4484, 1387, -10030, -6870, -264, 24342, -3258, 8265, -632, 21648, 13048, 16222, -1152, -12834, 20476, 790, 3136, 28810, 4366, 25764, 1368, 15100, -13962, -9385, -7008, 1353, 1888, 1547, 48, 13008, 6042, -8155, 17864, 235, 19050, 2138, -2296, -5499, 7916, 2261, 4048, -8434, 15300, 14304, -4800, -11654, -3036, -21097, -9924, -16992, -2556, -16436, 2504, -23196, -16308, 432, 560, 1413, 646, 6519, 3392, -18736, 8132, -18941, -9468, -4104, -1806, -28667, -12168, -1830, -292, 16702, 12000, 14078, 14628, 23462, 1024, 3591, -23256, -11130, 13208, 715, 4720, 13902, -12000, -18392, -13728, 13947, -5940, -40115, 9102, -5268, -640, -15501, 7248, 4912, -1368, 4320, -15848, 20382, 9784, 19940, -20468, 2118, -14352, -14579, -5950, -41254, -2560, 41508, -29482, -16592, 15312, 40063, -52, 57, 6424, -3682, 7074, 3996, -12524, -8663, -24032, 9076, 8304, 1892, 4268, 19218, -17368, 24942, 1662, -5022, 1600, -17064, -5700, 39760, 1320, 45185, -2020, 17155, 1472, -8202, -12960, 882, 9144, -22294, 19092, 10982, 3024, -44844, -4082, -1589, 11592, 4028, -2892, 32804, 3072, 9808, -1388, -24045, 8612, 729, 13578, 38528, 12168, -20650, -14230, -11230, 7440, 13026, -13276, 28294, 1216, 20355, -27126, -36996, -6308, 37003, 3448, -2820, 56, -6189, -1100, -17922, 15456, 18761, 26696, 29572, 8816, -12436, 16966, -760, 992, -5636, 41502, -49955, 10800, -25607, -9990, -41970, -19460, 34674, -1584, 40406, -1152, -39026, -12586, -7041, -10220, -55374, -3040, -20970, 9136, 3352, 27646, 19300, -17504, -25827, -34398, 18837, -800, -56097, 27734, 21223, 2472, -20397, 11626, -26931, -5360, 9861, -13980, -9855, 1608, 28190, 5856, 1391, -7264, -3110, 29240, 35883, 7676, -27447, -11924, -26538, 4632, -30071, -6816, 28800, 1748, 1827, -9756, -42620, 10832, -2295, -28032, 26133, -3216, 8293, 22346, -19089, -6024, 1270, 9942, 50496, -20052, -25934, 26938, 3648, -1088, 75822, 33750, 4808, -1516, -28904, -27204, -3528, -1888, -13140, 22102, 9684, 1048, 13401, -26688, 20902, -17424, -10580, 1444, -22964, -28624, -20517, -23570, 25804, -16408, -46294, 36894, -27591, 21840, 45450, 2168, -51804, 2336, -13206, 5420, 18873, 8808, 10469, 16978, 14376, -5216, -29289, 2870, 56024, 2428, 26675, -15828, 59976, -6224, 16632, -19878, -69690, -21404, -46595, -14470, -3358, -1368, 23228, 45980, 58707, 4216, 49035, 5644, 9423, 2304, 74540, -5538, -70284, 13048, 5733, 20170, -30748, 10352, 5802, -6326, -950, -39264, 2534, -7738, -18879, 960, -4182, -21468, 10671, 8200, 29130, 552, 30904, 1064, 55330, -4094, 80256, 1816, -14671, -8626, 20743, 3808, -64472, 6288, -9929, 10772, 40296, -38152, -42914, -19328, 67968, -2394, 5577, 12156, 1395, -5308, 30204, -6928, 12863, -19712, -73190, -3480, 429, 21750, 1356, -11360, -6322, -2134, -8685, 20440, -63845, -36456, -34490, 1088, -7656, -6060, 15930, -1292, -20116, -14208, -18282, 31824, -32677, 24570, 9092, -7740, -32835, -55594, 24811, -19504, 20128, -13462, -6278, 20536, -3748, -38046, -20691, 1336, 13662, -4476, -62481, -15252, -4180, 9700, -33772, 6048, -48942, -9968, -23320, 18064, -13592, 27144, -26141, -8968, 48388, 2774, 10353, -20060, 29881, -13740, -14039, -528, 22635, 48684, -6577, -6516, 5100, 16530, -528, -1264, -64960, 43296, -11021, 26096, -7391, 32444, -57462, -2304, 51903, -25668, 34044, 40952, 47519, 1580, -83738, 6272, 59358, 57620, 18717, 8732, 10322, 51528, -33642, 2736, 12776, 30200, -96402, -27924, 29571, -18770, 7767, -14016, 35060, 2706, 56742, 3776, -16170, 3094, 36230, 96, 55383, 26016, 1140, 12084, 27581, -16310, -213, 35728, 19570, 470, 38867, 38100, -74813, 4276, 2920, -4592, 90108, -10998, 27364, 15832, -84095, 4522, 20337, 8096, 58242, -16868, -126069, 30600, 3006, 28608, -9048, -9600, 33554, -23308, -61480, -6072, 26712, -42194, 8000, -19848, -8227, -33984, 26664, -5112, -16059, -32872, 98813, 5008, 65952, -46392, -4856, -32616, -122282, 864, -42054, 1120, -79962, 2826, 114122, 1292, 28032, 13038, -7878, 6784, -37753, -37472, 1899, 16264, 11077, -37882, -7406, -18936], "hecke_ring_index_factorization": [], "nf_label": "2.2.73.1", "field_poly": [-18, -1, 1], "atkin_lehner_string": "--", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, -1], [19, -1]], "char_values": [38, 1, [21], [1]], "Nk2": 608, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 4, "trace_display": [4, 9, -9, -18], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+2q^{2}+(5-\\beta )q^{3}+4q^{4}+(-6+3\\beta )q^{5}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 73, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[3, [2, -9, 1]]], "space_label": "38.4.a", "level": 38, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 3, "hecke_orbit_code": 9007199321849894, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.040", "prec": 17}, {"__RealLiteral__": 0, "data": "1.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.144", "prec": 17}, {"__RealLiteral__": 0, "data": "9.691", "prec": 17}, {"__RealLiteral__": 0, "data": "0.734", "prec": 17}, {"__RealLiteral__": 0, "data": "68.148", "prec": 20}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0, 0], [1, 0], [2, 0], [5, -1], [4, 0], [-6, 3], [10, -2], [-11, 4], [8, 0], [16, -9], [-12, 6], [-8, -1], [20, -4], [15, -13], [-22, 8], [-84, 18], [16, 0], [-41, 2], [32, -18], [19, 0], [-24, 12], [-127, 27], [-16, -2], [43, -13], [40, -8], [73, -27], [30, -26], [107, -25], [-44, 16], [-9, 21], [-168, 36], [84, 44], [32, 0], [-22, 4], [-82, 4], [282, -45], [64, -36], [82, 28], [38, 0], [309, -67], [-48, 24], [-20, -10], [-254, 54], [342, -7], [-32, -4], [-582, 75], [86, -26], [-230, 71], [80, -16], [66, -72], [146, -54], [-241, 49], [60, -52], [-601, -17], [214, -50], [-6, -21], [-88, 32], [95, -19], [-18, 42], [-131, -25], [-336, 72], [212, -111], [168, 88], [-824, 127], [64, 0], [-792, 84], [-44, 8], [573, 77], [-164, 8], [449, -95], [564, -90], [158, -116], [128, -72], [97, 184], [164, 56], [851, -181], [76, 0], [16, -25], [618, -134], [646, 58], [-96, 48], [553, 36], [-40, -20], [-238, -194], [-508, 108], [354, -129], [684, -14], [-423, 93], [-64, -8], [-212, 188], [-1164, 150], [-1101, 151], [172, -52], [-372, 92], [-460, 142], [-114, 57], [160, -32], [698, -102], [132, -144], [34, 65], [292, -108]]}