# Stored data for newform 20.3.f.a, downloaded from the LMFDB on 25 April 2024.
{"label": "20.3.f.a", "space_label": "20.3.f", "level": 20, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 343647715348, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 61994869210134035, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": false, "Nk2": 180, "analytic_conductor": 0.5449605287205938, "hecke_ring_index": 1, "level_radical": 10, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.247", "prec": 17}, "analytic_rank_proved": true, "char_values": [20, 4, [11, 17], [4, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [13, 17], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.960", "prec": 17}, {"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "11.449", "prec": 20}, {"__RealLiteral__": 0, "data": "1.197", "prec": 17}, {"__RealLiteral__": 0, "data": "93.299", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c4", "trace_display": [0, 2, -6, -14], "traces": [0, 2, 0, 2, 0, -6, 0, -14, 0, 0, 0, 20, 0, 18, 0, 2, 0, 2, 0, 0, 0, -28, 0, -46, 0, -14, 0, 32, 0, 0, 0, -28, 0, 20, 0, 98, 0, 66, 0, 0, 0, -28, 0, -30, 0, -56, 0, -78, 0, 0, 0, 4, 0, -14, 0, -60, 0, -16, 0, 0, 0, 84, 0, 98, 0, 18, 0, -14, 0, 0, 0, 196, 0, 98, 0, -62, 0, -140, 0, 0, 0, -62, 0, -126, 0, -14, 0, -16, 0, 0, 0, -252, 0, -28, 0, 64, 0, 66, 0, 0, 0, 52, 0, 146, 0, 84, 0, 242, 0, 0, 0, 132, 0, -254, 0, -46, 0, 126, 0, 0, 0, -42, 0, -28, 0, 234, 0, -14, 0, 0, 0, -460, 0, -112, 0, -224, 0, -126, 0, 0, 0, -156, 0, 180, 0, 64, 0, 98, 0, 0, 0, 260, 0, -14, 0, 84, 0, -126, 0, 0, 0, 644, 0, 130, 0, 20, 0, -206, 0, 0, 0, 112, 0, 146, 0, -238, 0, -112, 0, 0, 0, -140, 0, 84, 0, -462, 0, 20, 0, 0, 0, -284, 0, -126, 0, 144, 0, -126, 0, 0, 0, -28, 0, -112, 0, 84, 0, -322, 0, 0, 0, 628, 0, 196, 0, -30, 0, 196, 0, 0, 0, 36, 0, -270, 0, 336, 0, 562, 0, 0, 0, -280, 0, 546, 0, 546, 0, 192, 0, 0, 0, -892, 0, -350, 0, -392, 0, -144, 0, 0, 0, -300, 0, -460, 0, -12, 0, 322, 0, 0, 0, 112, 0, -302, 0, -14, 0, -224, 0, 0, 0, 420, 0, -252, 0, -140, 0, 258, 0, 0, 0, -348, 0, 226, 0, 112, 0, 196, 0, 0, 0, 132, 0, 690, 0, 448, 0, 320, 0, 0, 0, 420, 0, 52, 0, -252, 0, -654, 0, 0, 0, 4, 0, 162, 0, 98, 0, -318, 0, 0, 0, 484, 0, 16, 0, -558, 0, -272, 0, 0, 0, -364, 0, -462, 0, 98, 0, -894, 0, 0, 0, -280, 0, 0, 0, -368, 0, 50, 0, 0, 0, 576, 0, 642, 0, -588, 0, -28, 0, 0, 0, 594, 0, -42, 0, 98, 0, 754, 0, 0, 0, 196, 0, 434, 0, 322, 0, -144, 0, 0, 0, -28, 0, 114, 0, 980, 0, -210, 0, 0, 0, -92, 0, -460, 0, -768, 0, 386, 0, 0, 0, -60, 0, -252, 0, 186, 0, 660, 0, 0, 0, -252, 0, -784, 0, -126, 0, -176, 0, 0, 0, -908, 0, 546, 0, 34, 0, -588, 0, 0, 0, -988, 0, -1022, 0, 112, 0, 368, 0, 0, 0, -686, 0, 354, 0, 896, 0, 336, 0, 0, 0, -280, 0, 260, 0, 756, 0, 1218, 0, 0, 0, 980, 0, -14, 0, -28, 0, 50, 0, 0, 0, -252, 0, -300, 0, -384, 0, -98, 0, 0, 0, 1188, 0, 644, 0, -462, 0, 498, 0, 0, 0, 1300, 0, 16, 0, -560, 0, -1372, 0, 0, 0, -412, 0, -942, 0, -156, 0, 14, 0, 0, 0, -1372, 0, 256, 0, 146, 0, -780, 0, 0, 0, -732, 0, 546, 0, 196, 0, -28, 0, 0, 0, 784, 0, -252, 0, -1694, 0, 112, 0, 0, 0, 788, 0, -140, 0, 1088, 0, -462, 0, 0, 0, -128, 0, 1344, 0, -396, 0, -1470, 0, 0, 0, 40, 0, 1218, 0, -254, 0, 434, 0, 0, 0, 1876, 0, -284, 0, 1426, 0, 194, 0, 0, 0, 1764, 0, -140, 0, -882, 0, -78, 0, 0, 0, -252, 0, -958, 0, 112, 0, 672, 0, 0, 0, -860, 0, 98, 0, 126, 0, -846, 0, 0, 0, -1404, 0, 498, 0, -28, 0, 642, 0, 0, 0, -1472, 0, -1568, 0, -1054, 0, -160, 0, 0, 0, -1276, 0, 628, 0, 98, 0, 882, 0, 0, 0, 964, 0, 66, 0, -240, 0, -14, 0, 0, 0, 392, 0, -942, 0, 1380, 0, 686, 0, 0, 0, -1484, 0, 36, 0, -112, 0, 368, 0, 0, 0, 840, 0, -574, 0, 544, 0, 1154, 0, 0, 0, 1124, 0, -798, 0, 882, 0, 336, 0, 0, 0, 756, 0, 980, 0, 704, 0, -28, 0, 0, 0, -940, 0, 528, 0, 468, 0, -364, 0, 0, 0, -1344, 0, 644, 0, 180, 0, -576, 0, 0, 0, -2044, 0, -892, 0, -384, 0, 882, 0, 0, 0, -60, 0, 722, 0, -686, 0, -140, 0, 0, 0, -288, 0, -686, 0, -1344, 0, -882, 0, 0, 0, 1572, 0, -300, 0, -780, 0, -126, 0, 0, 0, -796, 0, -1904, 0, -14, 0, -1008, 0, 0, 0, 644, 0, 1650, 0, 196, 0, -924, 0, 0, 0, 1960, 0, 256, 0, 882, 0, -142, 0, 0, 0, 3556, 0, 756, 0, -112, 0, 66, 0, 0, 0, 1568, 0, 980, 0, -1932, 0, 752, 0, 0, 0, -1772, 0, 420, 0, 130, 0, 240, 0, 0, 0, -1228, 0, 2002, 0, -620, 0, -1230, 0, 0, 0, 516, 0, -98, 0, 1442, 0, -448, 0, 0, 0, 1554, 0, -348, 0, -56, 0, 294, 0, 0, 0, -3036, 0, -1870, 0, -336, 0, -126, 0, 0, 0, 392, 0, 434, 0, 146, 0, -574, 0, 0, 0, -252, 0, -462, 0, -1022, 0, -1662, 0, 0, 0, 644, 0, -574, 0, 784, 0, -1806, 0, 0, 0, -620, 0, -624, 0, -448, 0, 828, 0, 0, 0, -28, 0, 420, 0, 420, 0, 2162, 0, 0, 0, -476, 0, -1260, 0, 84, 0, 3220, 0, 0, 0, -1308, 0, 1764, 0, 1122, 0, 1022, 0, 0, 0, 784, 0, 4, 0, -140, 0, -766, 0, 0, 0, 84, 0, 644, 0, 1792, 0, 2674, 0, 0, 0, -636, 0, 546, 0, 852, 0, -160, 0, 0, 0, -1530, 0, -1694, 0, -126, 0, -1486, 0, 0, 0, 532, 0, -1232, 0, -864, 0, 834, 0, 0, 0, 1904, 0, -1262, 0, 882, 0, 1092, 0, 0, 0, -28, 0, -364, 0, -2688, 0, -1342, 0, 0, 0], "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, 5, 3, -1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "20.3.f.a", "char_is_minimal": true, "conrey_index": 13, "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], [1, 0], [0, 0], [1, -1], [0, 0], [-3, 4], [0, 0], [-7, -7], [0, 0], [0, 7], [0, 0], [10, 0], [0, 0], [9, -9], [0, 0], [1, 7], [0, 0], [1, 1], [0, 0], [0, -8], [0, 0], [-14, 0], [0, 0], [-23, 23], [0, 0], [-7, -24], [0, 0], [16, 16], [0, 0], [0, -8], [0, 0], [-14, 0], [0, 0], [10, -10], [0, 0], [49, -7], [0, 0], [33, 33], [0, 0], [0, -18], [0, 0], [-14, 0], [0, 0], [-15, 15], [0, 0], [-28, -21], [0, 0], [-39, -39], [0, 0], [0, 49], [0, 0], [2, 0], [0, 0], [-7, 7], [0, 0], [-30, 40], [0, 0], [-8, -8], [0, 0], [0, -56], [0, 0], [42, 0], [0, 0], [49, -49], [0, 0], [9, 63], [0, 0], [-7, -7], [0, 0], [0, 46], [0, 0], [98, 0], [0, 0], [49, -49], [0, 0], [-31, -17], [0, 0], [-70, -70], [0, 0], [0, 96], [0, 0], [-31, 0], [0, 0], [-63, 63], [0, 0], [-7, 1], [0, 0], [-8, -8], [0, 0], [0, -112], [0, 0], [-126, 0], [0, 0], [-14, 14], [0, 0], [32, 24], [0, 0], [33, 33], [0, 0], [0, 70], [0, 0]]}