# Stored data for newform 189.4.a.a, downloaded from the LMFDB on 11 October 2024.
{"Nk2": 3024, "analytic_conductor": 11.151360991084976, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [189, 1, [29, 136], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [3, 1]], [5, [-12, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 67109053, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "189.4.a.a", "level": 189, "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": [3, 7], "level_radical": 21, "minimal_twist": "189.4.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-3q^{2}+q^{4}+12q^{5}+7q^{7}+21q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "189.4.a", "trace_display": [-3, 0, 12, 7], "trace_hash": 594930921335630728, "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.974", "prec": 17}, {"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "1.896", "prec": 17}, {"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "4.638", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 1, -3, 0, 1, 12, 0, 7, 21, 0, -36, -12, 0, -61, -21, 0, -71, 117, 0, 2, 12, 0, 36, 75, 0, 19, 183, 0, 7, -3, 0, 263, 45, 0, -351, 84, 0, 218, -6, 0, 252, 246, 0, 515, -12, 0, -225, -318, 0, 49, -57, 0, -61, 459, 0, -144, 147, 0, 9, 255, 0, -862, -789, 0, 433, -732, 0, 479, 117, 0, -252, 117, 0, -430, -654, 0, 2, -84, 0, -646, -852, 0, -738, 348, 0, 1404, -1545, 0, -252, 585, 0, -427, 75, 0, 954, 24, 0, -376, -147, 0, 19, 978, 0, -655, -1281, 0, -1377, 108, 0, 272, 432, 0, -497, -2256, 0, 900, -3, 0, -765, 819, 0, -1187, 2586, 0, 263, -1272, 0, 1784, -1659, 0, 2196, 1749, 0, 14, -1437, 0, 2457, 1374, 0, 2450, 84, 0, -351, 732, 0, -36, 1290, 0, 218, 921, 0, 650, 42, 0, 252, 3156, 0, -871, 1938, 0, 540, 525, 0, -3697, 246, 0, -1044, -1824, 0, 1524, -4212, 0, 515, 744, 0, 133, 852, 0, -1755, 4572, 0, -3481, 1281, 0, 1575, 2616, 0, -1404, -318, 0, -72, -3756, 0, -4867, 1128, 0, 49, 18, 0, -1807, 399, 0, -2934, -21, 0, 2952, 1965, 0, 4331, -24, 0, -4273, 459, 0, -324, 6180, 0, 1841, -816, 0, -144, -7137, 0, 2648, 315, 0, 6768, -5493, 0, -790, -2700, 0, -63, -6228, 0, -3816, 255, 0, -2457, -4812, 0, 1622, 3561, 0, -862, 588, 0, -122, 5523, 0, 3816, 2880, 0, -900, -5352, 0, 1513, 2190, 0, 1526, -732, 0, -5247, 1869, 0, 5508, -42, 0, 479, 2268, 0, 2027, -8307, 0, -4122, -228, 0, 3944, -7350, 0, 1764, -4602, 0, -3220, 117, 0, -2196, 1722, 0, 8776, 108, 0, -430, -6810, 0, 3060, 4578, 0, -2763, -4575, 0, 3605, -1950, 0, -142, -10344, 0, 758, -84, 0, -9468, 9480, 0, 3350, 2613, 0, -646, -426, 0, 36, 5196, 0, -1575, 234, 0, -1159, 11091, 0, 5166, -2226, 0, -3103, 348, 0, 5472, 5748, 0, -11725, -4572, 0, 1404, -3156, 0, 343, 10815, 0, -2232, 1506, 0, 10289, -399, 0, -540, -12693, 0, 1404, 585, 0, -13716, -5031, 0, -6855, 10443, 0, -427, -5160, 0, 9479, -5325, 0, -7848, 3213, 0, -8566, 4212, 0, -6678, 183, 0, -2320, 24, 0, 11268, 1092, 0, -1008, 14601, 0, -376, 12570, 0, 8775, 1029, 0, -54, -7752, 0, -6802, 5421, 0, -1349, 8526, 0, -16043, 978, 0, 63, -2616, 0, 13466, -8856, 0, -655, 1785, 0, 4176, -2745, 0, 72, 15339, 0, -4102, 12819, 0, 9639, 2223, 0, -6034, 108, 0, -18540, 2592, 0, -9448, -5523, 0, 272, 150, 0, 11369, -3024, 0, 21411, 10842, 0, 7020, -7944, 0, 3031, -13140, 0, -2952, -2256, 0, 16479, -5124, 0, 1379, 2370, 0, 900, -678, 0, 15734, 213, 0, 18684, 7416, 0, 3353, 11448, 0, 5355, -6180, 0, 38, 819, 0, 14436, 1248, 0, -13298, -4866, 0, -1187, -4512, 0, -20950, -18102, 0, -1764, 768, 0, -351, 366, 0, -18673, 819, 0, 4772, -1272, 0, -8640, -11088, 0, 11736, 2700, 0, 1784, -16854, 0, -3010, 8733, 0, -6570, -7860, 0, 3816, -4578, 0, -15372, -3195, 0, 920, 1749, 0, -5607, 30771, 0, -6542, -16524, 0, 14, -15006, 0, 1296, 10059, 0, -6804, -588, 0, -7180, -6081, 0, 5265, 3264, 0, 11612, 1374, 0, 684, -6, 0, -4522, -11832, 0, 2450, -9819, 0, -31415, -5964, 0, 13806, -15801, 0, -27072, 9660, 0, 2457, 8340, 0, 1073, 732, 0, -5166, 1425, 0, 22466, -26328, 0, -36, 2436, 0, -5508, -9030, 0, 20430, 3219, 0, 526, -9180, 0, -15478, 9342, 0, 9828, 921, 0, 13725, -6927, 0, -15172, -10815, 0, 650, -14244, 0, -4921, 90, 0, 31032, 19398, 0, 218, -2274, 0, -1764, 22350, 0, 9290, 3156, 0, -28440, 4095, 0, -17639, -10050, 0, -871, 25506, 0, 13988, -13566, 0, 1278, 21408, 0, -2989, -108, 0, -19908, -11388, 0, 9956, 525, 0, -702, -7830, 0, -3060, 3477, 0, -3697, -3633, 0, 20988, -17466, 0, 6678, 6036, 0, -5110, 9309, 0, 7308, 168, 0, -225, -1824, 0, -17244, 10344, 0, -12553, 35175, 0, 1524, -22872, 0, -2632, 29484, 0, 9468, 21672, 0, 16488, -1029, 0, -36565, -27999, 0, 17120, 744, 0, -4518, 29400, 0, 28782, -30867, 0, 133, -5562, 0, 436, -5196, 0, 38079, 6846, 0, 16256, -4212, 0, 12285, 19725, 0, 8784, 4572, 0, 15093, 20016, 0, -4585, 20565, 0, -3481, -57, 0, 3539, -8967, 0, 15480, 60255, 0, -19663, -28437, 0, 3375, -5748, 0, -17116, 2616, 0, -9639, -31641, 0, 11052, 25698, 0, -1404, 756, 0, -17314, 22578, 0, -549, 7800, 0, 12476, 6960, 0, 504, 21855, 0, 1904, -3756, 0, -3276, -15555, 0, -5812, 3024, 0, -4867, 252, 0, 4997, -7896, 0, -37710, 492, 0, -1404, -26325, 0, -3479, -10452, 0, -12886, 18, 0, 23256, -15792, 0, 52582, 20406, 0, -1807, 39342, 0, -37206, 855, 0, -25578, 5160, 0, 6300, 48129, 0, 20538, -33264, 0, -10258, -21, 0, 7848, -44364, 0, 1030, -40398, 0, 2952, 33063, 0, -13102, -13755, 0, -5355, -25182, 0, -17170, -12528, 0, -26413, 5733, 0, -21888, -24, 0, -46017, -4458, 0, -24380, 12306, 0, -4273, 18288, 0, -8309, -32589, 0, -6669, 16350, 0, 39773, 18102, 0, 2268, 4191, 0, 19946, 6180, 0, -7776, -41067, 0, 8928, 28344, 0, 1841, 7752, 0, -29219, 5712, 0, -450, -8904, 0, -32056, -34107, 0, 10224, 1899, 0, 8021, -7137, 0, -32526, -6540, 0, 12488, -21060, 0, 2648, -636, 0, 54864, -11613, 0, 39420, -789, 0, 53703, 8856, 0, -47376, -41772, 0, 5780, -5493, 0, 15372, -27480, 0, -4176, -4137, 0, -790, 12243, 0, -7450, 18900, 0, 2034, -7137, 0, 4142, -47202, 0, -135, 7602, 0, 98, -6228, 0, -22248, -16848, 0, -6316, -10059, 0, -3816, -25170, 0, 18450, -18105, 0, 18540, -20874, 0, 26230, -114, 0, 17199, 31824, 0, -45072, -4812, 0, -3744, 9618, 0, 39378, 39894, 0, 1622, -58404, 0, 7040, -24927, 0, 13536, 27189, 0, 17150, 62850, 0, 61202, 33438, 0, -7020, 588, 0, -2304, -16212, 0, 216, 1053, 0, -122, 38625, 0, 24194, 11835, 0, -2457, -21684, 0, -27565, -14316, 0, -26712], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, -3, 0, 1, 12, 0, 7, 21, 0, -36, -12, 0, -61, -21, 0, -71, 117, 0, 2, 12, 0, 36, 75, 0, 19, 183, 0, 7, -3, 0, 263, 45, 0, -351, 84, 0, 218, -6, 0, 252, 246, 0, 515, -12, 0, -225, -318, 0, 49, -57, 0, -61, 459, 0, -144, 147, 0, 9, 255, 0, -862, -789, 0, 433, -732, 0, 479, 117, 0, -252, 117, 0, -430, -654, 0, 2, -84, 0, -646, -852, 0, -738, 348, 0, 1404, -1545, 0, -252, 585, 0, -427, 75, 0, 954, 24, 0, -376, -147, 0, 19, 978, 0, -655, -1281, 0, -1377, 108, 0, 272, 432, 0, -497, -2256, 0, 900, -3, 0, -765, 819, 0, -1187, 2586, 0, 263, -1272, 0, 1784, -1659, 0, 2196, 1749, 0, 14, -1437, 0, 2457, 1374, 0, 2450, 84, 0, -351, 732, 0, -36, 1290, 0, 218, 921, 0, 650, 42, 0, 252, 3156, 0, -871, 1938, 0, 540, 525, 0, -3697, 246, 0, -1044, -1824, 0, 1524, -4212, 0, 515, 744, 0, 133, 852, 0, -1755, 4572, 0, -3481, 1281, 0, 1575, 2616, 0, -1404, -318, 0, -72, -3756, 0, -4867, 1128, 0, 49, 18, 0, -1807, 399, 0, -2934, -21, 0, 2952, 1965, 0, 4331, -24, 0, -4273, 459, 0, -324, 6180, 0, 1841, -816, 0, -144, -7137, 0, 2648, 315, 0, 6768, -5493, 0, -790, -2700, 0, -63, -6228, 0, -3816, 255, 0, -2457, -4812, 0, 1622, 3561, 0, -862, 588, 0, -122, 5523, 0, 3816, 2880, 0, -900, -5352, 0, 1513, 2190, 0, 1526, -732, 0, -5247, 1869, 0, 5508, -42, 0, 479, 2268, 0, 2027, -8307, 0, -4122, -228, 0, 3944, -7350, 0, 1764, -4602, 0, -3220, 117, 0, -2196, 1722, 0, 8776, 108, 0, -430, -6810, 0, 3060, 4578, 0, -2763, -4575, 0, 3605, -1950, 0, -142, -10344, 0, 758, -84, 0, -9468, 9480, 0, 3350, 2613, 0, -646, -426, 0, 36, 5196, 0, -1575, 234, 0, -1159, 11091, 0, 5166, -2226, 0, -3103, 348, 0, 5472, 5748, 0, -11725, -4572, 0, 1404, -3156, 0, 343, 10815, 0, -2232, 1506, 0, 10289, -399, 0, -540, -12693, 0, 1404, 585, 0, -13716, -5031, 0, -6855, 10443, 0, -427, -5160, 0, 9479, -5325, 0, -7848, 3213, 0, -8566, 4212, 0, -6678, 183, 0, -2320, 24, 0, 11268, 1092, 0, -1008, 14601, 0, -376, 12570, 0, 8775, 1029, 0, -54, -7752, 0, -6802, 5421, 0, -1349, 8526, 0, -16043, 978, 0, 63, -2616, 0, 13466, -8856, 0, -655, 1785, 0, 4176, -2745, 0, 72, 15339, 0, -4102, 12819, 0, 9639, 2223, 0, -6034, 108, 0, -18540, 2592, 0, -9448, -5523, 0, 272, 150, 0, 11369, -3024, 0, 21411, 10842, 0, 7020, -7944, 0, 3031, -13140, 0, -2952, -2256, 0, 16479, -5124, 0, 1379, 2370, 0, 900, -678, 0, 15734, 213, 0, 18684, 7416, 0, 3353, 11448, 0, 5355, -6180, 0, 38, 819, 0, 14436, 1248, 0, -13298, -4866, 0, -1187, -4512, 0, -20950, -18102, 0, -1764, 768, 0, -351, 366, 0, -18673, 819, 0, 4772, -1272, 0, -8640, -11088, 0, 11736, 2700, 0, 1784, -16854, 0, -3010, 8733, 0, -6570, -7860, 0, 3816, -4578, 0, -15372, -3195, 0, 920, 1749, 0, -5607, 30771, 0, -6542, -16524, 0, 14, -15006, 0, 1296, 10059, 0, -6804, -588, 0, -7180, -6081, 0, 5265, 3264, 0, 11612, 1374, 0, 684, -6, 0, -4522, -11832, 0, 2450, -9819, 0, -31415, -5964, 0, 13806, -15801, 0, -27072, 9660, 0, 2457, 8340, 0, 1073, 732, 0, -5166, 1425, 0, 22466, -26328, 0, -36, 2436, 0, -5508, -9030, 0, 20430, 3219, 0, 526, -9180, 0, -15478, 9342, 0, 9828, 921, 0, 13725, -6927, 0, -15172, -10815, 0, 650, -14244, 0, -4921, 90, 0, 31032, 19398, 0, 218, -2274, 0, -1764, 22350, 0, 9290, 3156, 0, -28440, 4095, 0, -17639, -10050, 0, -871, 25506, 0, 13988, -13566, 0, 1278, 21408, 0, -2989, -108, 0, -19908, -11388, 0, 9956, 525, 0, -702, -7830, 0, -3060, 3477, 0, -3697, -3633, 0, 20988, -17466, 0, 6678, 6036, 0, -5110, 9309, 0, 7308, 168, 0, -225, -1824, 0, -17244, 10344, 0, -12553, 35175, 0, 1524, -22872, 0, -2632, 29484, 0, 9468, 21672, 0, 16488, -1029, 0, -36565, -27999, 0, 17120, 744, 0, -4518, 29400, 0, 28782, -30867, 0, 133, -5562, 0, 436, -5196, 0, 38079, 6846, 0, 16256, -4212, 0, 12285, 19725, 0, 8784, 4572, 0, 15093, 20016, 0, -4585, 20565, 0, -3481, -57, 0, 3539, -8967, 0, 15480, 60255, 0, -19663, -28437, 0, 3375, -5748, 0, -17116, 2616, 0, -9639, -31641, 0, 11052, 25698, 0, -1404, 756, 0, -17314, 22578, 0, -549, 7800, 0, 12476, 6960, 0, 504, 21855, 0, 1904, -3756, 0, -3276, -15555, 0, -5812, 3024, 0, -4867, 252, 0, 4997, -7896, 0, -37710, 492, 0, -1404, -26325, 0, -3479, -10452, 0, -12886, 18, 0, 23256, -15792, 0, 52582, 20406, 0, -1807, 39342, 0, -37206, 855, 0, -25578, 5160, 0, 6300, 48129, 0, 20538, -33264, 0, -10258, -21, 0, 7848, -44364, 0, 1030, -40398, 0, 2952, 33063, 0, -13102, -13755, 0, -5355, -25182, 0, -17170, -12528, 0, -26413, 5733, 0, -21888, -24, 0, -46017, -4458, 0, -24380, 12306, 0, -4273, 18288, 0, -8309, -32589, 0, -6669, 16350, 0, 39773, 18102, 0, 2268, 4191, 0, 19946, 6180, 0, -7776, -41067, 0, 8928, 28344, 0, 1841, 7752, 0, -29219, 5712, 0, -450, -8904, 0, -32056, -34107, 0, 10224, 1899, 0, 8021, -7137, 0, -32526, -6540, 0, 12488, -21060, 0, 2648, -636, 0, 54864, -11613, 0, 39420, -789, 0, 53703, 8856, 0, -47376, -41772, 0, 5780, -5493, 0, 15372, -27480, 0, -4176, -4137, 0, -790, 12243, 0, -7450, 18900, 0, 2034, -7137, 0, 4142, -47202, 0, -135, 7602, 0, 98, -6228, 0, -22248, -16848, 0, -6316, -10059, 0, -3816, -25170, 0, 18450, -18105, 0, 18540, -20874, 0, 26230, -114, 0, 17199, 31824, 0, -45072, -4812, 0, -3744, 9618, 0, 39378, 39894, 0, 1622, -58404, 0, 7040, -24927, 0, 13536, 27189, 0, 17150, 62850, 0, 61202, 33438, 0, -7020, 588, 0, -2304, -16212, 0, 216, 1053, 0, -122, 38625, 0, 24194, 11835, 0, -2457, -21684, 0, -27565, -14316, 0, -26712]}