# Stored data for newform 189.3.b.b, downloaded from the LMFDB on 25 April 2024. {"label": "189.3.b.b", "space_label": "189.3.b", "level": 189, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503668397179069, "dim": 4, "is_polredabs": true, "nf_label": "4.0.12544.1", "trace_hash": 363122230014547320, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [9, 0, 8, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{2}q^{4}-\\beta _{3}q^{5}+\\beta _{2}q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 1701, "analytic_conductor": 5.149876996409612, "hecke_ring_index": 3, "level_radical": 21, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [189, 2, [29, 136], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [134], "field_disc": 12544, "field_disc_factorization": [[2, 8], [7, 2]], "field_poly": [9, 0, 8, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.671", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.809", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1716.951", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -12, 0, 0, -36, 0, 0, 24, 0, 0, -32, 0, 0, 36, 0, 0, 28, 0, 0, 64, 0, 0, -12, 0, 0, -92, 0, 0, 72, 0, 0, -28, 0, 0, 24, 0, 0, 28, 0, 0, 140, 0, 0, -244, 0, 0, -284, 0, 0, 96, 0, 0, -32, 0, 0, 156, 0, 0, 56, 0, 0, 196, 0, 0, -28, 0, 0, -484, 0, 0, 356, 0, 0, -60, 0, 0, 180, 0, 0, 140, 0, 0, 180, 0, 0, 16, 0, 0, -140, 0, 0, 80, 0, 0, -456, 0, 0, -32, 0, 0, 112, 0, 0, 372, 0, 0, -660, 0, 0, -588, 0, 0, 196, 0, 0, 388, 0, 0, 268, 0, 0, -28, 0, 0, 36, 0, 0, -200, 0, 0, -636, 0, 0, 260, 0, 0, -392, 0, 0, 536, 0, 0, 308, 0, 0, 660, 0, 0, 476, 0, 0, -108, 0, 0, 396, 0, 0, 60, 0, 0, -420, 0, 0, -140, 0, 0, 220, 0, 0, -1080, 0, 0, -324, 0, 0, -276, 0, 0, -32, 0, 0, 80, 0, 0, 0, 0, 0, -236, 0, 0, 692, 0, 0, -656, 0, 0, 668, 0, 0, -144, 0, 0, 148, 0, 0, 196, 0, 0, -392, 0, 0, 300, 0, 0, 1072, 0, 0, -472, 0, 0, -828, 0, 0, -108, 0, 0, 84, 0, 0, 308, 0, 0, -952, 0, 0, -212, 0, 0, -144, 0, 0, 1560, 0, 0, 196, 0, 0, -392, 0, 0, -308, 0, 0, 240, 0, 0, -28, 0, 0, 144, 0, 0, -324, 0, 0, 276, 0, 0, 252, 0, 0, 264, 0, 0, 1636, 0, 0, 1084, 0, 0, -644, 0, 0, 228, 0, 0, -1344, 0, 0, -420, 0, 0, -328, 0, 0, -1656, 0, 0, 456, 0, 0, -1468, 0, 0, -252, 0, 0, 188, 0, 0, -420, 0, 0, -808, 0, 0, 1368, 0, 0, 272, 0, 0, 688, 0, 0, 780, 0, 0, -84, 0, 0, 0, 0, 0, -1552, 0, 0, 1632, 0, 0, 2240, 0, 0, -408, 0, 0, -1372, 0, 0, -1272, 0, 0, -84, 0, 0, -284, 0, 0, -876, 0, 0, 824, 0, 0, 468, 0, 0, 2284, 0, 0, -128, 0, 0, -392, 0, 0, -1064, 0, 0, 396, 0, 0, 1072, 0, 0, -1496, 0, 0, -884, 0, 0, 788, 0, 0, 308, 0, 0, 1220, 0, 0, 1428, 0, 0, 1476, 0, 0, -500, 0, 0, 716, 0, 0, -1152, 0, 0, -952, 0, 0, -868, 0, 0, -900, 0, 0, 700, 0, 0, -2120, 0, 0, 456, 0, 0, -1000, 0, 0, -252, 0, 0, -1556, 0, 0, 1608, 0, 0, -732, 0, 0, 672, 0, 0, 360, 0, 0, -384, 0, 0, -28, 0, 0, -1548, 0, 0, 356, 0, 0, 2772, 0, 0, -1684, 0, 0, -644, 0, 0, 540, 0, 0, 28, 0, 0, -24, 0, 0, 208, 0, 0, 972, 0, 0, -536, 0, 0, 1780, 0, 0, 532, 0, 0, -644, 0, 0, -760, 0, 0, 108, 0, 0, 1044, 0, 0, 708, 0, 0, -896, 0, 0, -188, 0, 0, 168, 0, 0, 908, 0, 0, 1560, 0, 0, 548, 0, 0, 588, 0, 0, 768, 0, 0, -1828, 0, 0, -252, 0, 0, 280, 0, 0, -2016, 0, 0, -100, 0, 0, -16, 0, 0, -864, 0, 0, -64, 0, 0, -56, 0, 0, -144, 0, 0, 1372, 0, 0, -408, 0, 0, 284, 0, 0, 188, 0, 0, -740, 0, 0, -84, 0, 0, -2172, 0, 0, 1252, 0, 0, 168, 0, 0, -40, 0, 0, -1808, 0, 0, -192, 0, 0, 1008, 0, 0, -324, 0, 0, -1428, 0, 0, -576, 0, 0, -532, 0, 0, 380, 0, 0, 900, 0, 0, -84, 0, 0, 1368, 0, 0, -1672, 0, 0, -156, 0, 0, -1068, 0, 0, 1652, 0, 0, 2660, 0, 0, -252, 0, 0, 1836, 0, 0, -684, 0, 0, -708, 0, 0, 100, 0, 0, 2280, 0, 0, -840, 0, 0, -1064, 0, 0, 1644, 0, 0, 1404, 0, 0, -1428, 0, 0, 824, 0, 0, -1828, 0, 0, -300, 0, 0, 252, 0, 0, -160, 0, 0, 1204, 0, 0, -1544, 0, 0, 1440, 0, 0, -1228, 0, 0, 716, 0, 0, 1428, 0, 0, -616, 0, 0, -2704, 0, 0, -1092, 0, 0, 268, 0, 0, -3192, 0, 0, 2728, 0, 0, 672, 0, 0, 336, 0, 0, -84, 0, 0, 276, 0, 0, 2392, 0, 0, 2408, 0, 0, 180, 0, 0, 700, 0, 0, 1680, 0, 0, -2428, 0, 0, -840, 0, 0, -404, 0, 0, -264, 0, 0, -3540, 0, 0, -252, 0, 0, 2616, 0, 0, -988, 0, 0, -5048, 0, 0, 2128, 0, 0, 72, 0, 0, 2124, 0, 0, 672, 0, 0, -396, 0, 0, 812, 0, 0, -3576, 0, 0, 252, 0, 0, -2380, 0, 0, 352, 0, 0, 1092, 0, 0, 1340, 0, 0, -1164, 0, 0, -1432, 0, 0, 2400, 0, 0, -2244, 0, 0, 560, 0, 0, -644, 0, 0, -528, 0, 0, -880, 0, 0, -612, 0, 0, 1088, 0, 0, 2064, 0, 0, 388, 0, 0, 448, 0, 0, -608, 0, 0, 564, 0, 0, -672, 0, 0, 628, 0, 0, -1408, 0, 0, 2472, 0, 0, 532, 0, 0, 2912, 0, 0, -2492, 0, 0, -408, 0, 0, -216, 0, 0, 2160, 0, 0, 4016, 0, 0, -28, 0, 0, 7092, 0, 0, -2016, 0, 0, -4456, 0, 0, 584, 0, 0, 1132, 0, 0, 476, 0, 0, 168, 0, 0, 3228, 0, 0, 2176, 0, 0, -756, 0, 0, 2868, 0, 0, -4396, 0, 0, -3808, 0, 0, 252, 0, 0, -2740, 0, 0, -2368, 0, 0, -1448, 0, 0, -2268, 0, 0, -1368, 0, 0, -2112, 0, 0, 280, 0, 0, -4672, 0, 0, -3340, 0, 0, -4468, 0, 0, 2504, 0, 0, 924, 0, 0, 4940, 0, 0, 1680, 0, 0, 1320, 0, 0, 1188], "weight_parity": -1, "has_non_self_twist": 1, "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], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "189.3.b.b", "char_is_minimal": true, "conrey_index": 134, "id": 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], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, 1, 0], [0, 2, 0, 1], [0, 0, 0, 0], [1, 0, 2, 0], [0, 3, 0, -4], [0, 0, 0, 0], [-3, 0, 5, 0], [0, -2, 0, 1], [0, 0, 0, 0], [-9, 0, 4, 0], [0, 1, 0, -1], [0, 0, 0, 0], [6, 0, -1, 0], [0, -3, 0, -2], [0, 0, 0, 0], [-8, 0, 11, 0], [0, -3, 0, 6], [0, 0, 0, 0], [9, 0, -5, 0], [0, -13, 0, 5], [0, 0, 0, 0], [7, 0, 0, 0], [0, 17, 0, 3], [0, 0, 0, 0], [16, 0, 7, 0], [0, -9, 0, 8], [0, 0, 0, 0], [-3, 0, 3, 0], [0, -3, 0, -2], [0, 0, 0, 0], [-23, 0, -14, 0], [0, 8, 0, -1], [0, 0, 0, 0], [18, 0, 9, 0], [0, -20, 0, -9], [0, 0, 0, 0], [-7, 0, -15, 0], [0, -18, 0, -5], [0, 0, 0, 0], [6, 0, -15, 0], [0, -11, 0, -1], [0, 0, 0, 0], [7, 0, 0, 0], [0, 19, 0, -5], [0, 0, 0, 0], [35, 0, -3, 0], [0, 28, 0, 2], [0, 0, 0, 0], [-61, 0, -14, 0], [0, -1, 0, 4], [0, 0, 0, 0], [-71, 0, 11, 0], [0, 41, 0, 1], [0, 0, 0, 0], [24, 0, -34, 0], [0, 2, 0, 7], [0, 0, 0, 0], [-8, 0, -9, 0], [0, -15, 0, -7], [0, 0, 0, 0], [39, 0, -1, 0], [0, -5, 0, -1], [0, 0, 0, 0], [14, 0, 1, 0], [0, 42, 0, -9], [0, 0, 0, 0], [49, 0, -23, 0], [0, 5, 0, -14], [0, 0, 0, 0], [-7, 0, 6, 0], [0, -18, 0, -5], [0, 0, 0, 0], [-121, 0, -9, 0], [0, -12, 0, 1], [0, 0, 0, 0], [89, 0, -2, 0], [0, -31, 0, 25], [0, 0, 0, 0], [-15, 0, -3, 0], [0, 23, 0, -15], [0, 0, 0, 0], [45, 0, 36, 0], [0, -10, 0, -15], [0, 0, 0, 0], [35, 0, -3, 0], [0, 24, 0, 9], [0, 0, 0, 0], [45, 0, -9, 0], [0, 3, 0, -4], [0, 0, 0, 0], [4, 0, -38, 0], [0, 7, 0, 0], [0, 0, 0, 0], [-35, 0, 9, 0]]}