# Stored data for newform 160.3.h.a, downloaded from the LMFDB on 20 April 2024. {"label": "160.3.h.a", "space_label": "160.3.h", "level": 160, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 481086668960, "dim": 6, "is_polredabs": true, "nf_label": "6.0.1827904.1", "trace_hash": 1898743986081578183, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [8, -16, 2, 1]]], "qexp_display": "q+(-1-\\beta _{1})q^{3}-\\beta _{4}q^{5}+(-2-\\beta _{3}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 20, "char_orbit_label": "h", "char_is_real": true, "Nk2": 1440, "analytic_conductor": 4.35968422976475, "hecke_ring_index": 512, "level_radical": 10, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [160, 2, [31, 101, 97], [1, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [159], "field_disc": -1827904, "field_disc_factorization": [[-1, 1], [2, 6], [13, 4]], "field_poly": [1, 0, 14, 0, 9, 0, 1], "hecke_ring_index_factorization": [[2, 9]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "5.580", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "168.938", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7434.503", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "2.2.3.c2", "trace_display": [0, -4, -2, -12], "traces": [0, 6, 0, -4, 0, -2, 0, -12, 0, 18, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 8, 0, 68, 0, -10, 0, -184, 0, 44, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, -68, 0, 76, 0, -6, 0, -268, 0, -62, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, -100, 0, 172, 0, 0, 0, -308, 0, -184, 0, 0, 0, 0, 0, 284, 0, 0, 0, 0, 0, 238, 0, 204, 0, -32, 0, -584, 0, 76, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 332, 0, -124, 0, 136, 0, -324, 0, 220, 0, 0, 0, 0, 0, 220, 0, 0, 0, 0, 0, -394, 0, 392, 0, 334, 0, 68, 0, -120, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -376, 0, 0, 0, -292, 0, 388, 0, -4, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 488, 0, -804, 0, -608, 0, 164, 0, 182, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 204, 0, 136, 0, 416, 0, 448, 0, -48, 0, 0, 0, 0, 0, -832, 0, 0, 0, 0, 0, -696, 0, -88, 0, 300, 0, 1244, 0, -32, 0, 0, 0, 0, 0, -684, 0, 0, 0, 0, 0, -832, 0, -540, 0, -862, 0, 668, 0, -372, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 892, 0, 180, 0, -534, 0, 1664, 0, 72, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 0, 0, 1796, 0, 148, 0, 1024, 0, 504, 0, 796, 0, 0, 0, 0, 0, -1024, 0, 0, 0, 0, 0, -1252, 0, -2308, 0, 1504, 0, 344, 0, -442, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, -1400, 0, -776, 0, -660, 0, 1516, 0, -56, 0, 0, 0, 0, 0, -716, 0, 0, 0, 0, 0, 1672, 0, 1344, 0, -832, 0, -632, 0, 744, 0, 0, 0, 0, 0, -556, 0, 0, 0, 0, 0, 1024, 0, -744, 0, 1032, 0, 908, 0, -596, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, -1258, 0, 1372, 0, 32, 0, 580, 0, -1036, 0, 0, 0, 0, 0, -1020, 0, 0, 0, 0, 0, -1848, 0, 452, 0, -992, 0, -812, 0, -1668, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 1644, 0, -1664, 0, -1466, 0, -832, 0, 892, 0, 0, 0, 0, 0, 1492, 0, 0, 0, 0, 0, 2492, 0, 1068, 0, 576, 0, -1256, 0, 2496, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, -2682, 0, 2140, 0, 1916, 0, -1592, 0, -1604, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2836, 0, -1612, 0, -1536, 0, -2116, 0, 200, 0, 0, 0, 0, 0, 1920, 0, 0, 0, 0, 0, 1664, 0, 576, 0, -416, 0, -620, 0, 1992, 0, 0, 0, 0, 0, 1696, 0, 0, 0, 0, 0, 2248, 0, 1476, 0, 1276, 0, -676, 0, -20, 0, 0, 0, 0, 0, 284, 0, 0, 0, 0, 0, -2260, 0, -1508, 0, 264, 0, -3072, 0, -254, 0, 0, 0, 0, 0, 2916, 0, 0, 0, 0, 0, -1300, 0, 4856, 0, -1044, 0, -1028, 0, -1964, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3584, 0, 476, 0, -1920, 0, -1932, 0, 1020, 0, 0, 0, 0, 0, -668, 0, 0, 0, 0, 0, 2504, 0, -4352, 0, 2496, 0, -3316, 0, 3072, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, -1508, 0, 1364, 0, 2350, 0, 692, 0, -496, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, -3888, 0, 3176, 0, -1498, 0, -4416, 0, -832, 0, 0, 0, 0, 0, -612, 0, 0, 0, 0, 0, 2108, 0, 172, 0, -792, 0, 1780, 0, -480, 0, 0, 0, 0, 0, 1824, 0, 0, 0, 0, 0, 2364, 0, 1664, 0, 352, 0, 1608, 0, -3384, 0, 0, 0, 0, 0, 1416, 0, 0, 0, 0, 0, -2872, 0, -468, 0, -64, 0, -1416, 0, -2496, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 92, 0, -4160, 0, -1400, 0, 2664, 0, -948, 0, 0, 0, 0, 0, 832, 0, 0, 0, 0, 0, 872, 0, 1416, 0, -2292, 0, -1260, 0, -390, 0, 0, 0, 0, 0, -1828, 0, 0, 0, 0, 0, 832, 0, 2484, 0, 972, 0, 2900, 0, 4808, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 0, 0, -2708, 0, -1896, 0, 4896, 0, -1664, 0, 44, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, -3520, 0, -3568, 0, -544, 0, 3340, 0, 1288, 0, 0, 0, 0, 0, -4288, 0, 0, 0, 0, 0, 1892, 0, -448, 0, -440, 0, 3976, 0, 2220, 0, 0, 0, 0, 0, -1084, 0, 0, 0, 0, 0, 2300, 0, -988, 0, 2624, 0, -1940, 0, -4580, 0, 0, 0, 0, 0, 1020, 0, 0, 0, 0, 0, -286, 0, 1736, 0, -2002, 0, 4116, 0, 2440, 0, 0, 0, 0, 0, -4064, 0, 0, 0, 0, 0, 464, 0, 148, 0, -2336, 0, 1404, 0, -2688, 0, 0, 0, 0, 0, -1396, 0, 0, 0, 0, 0, 3356, 0, -3012, 0, -4064, 0, 2932, 0, 488, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, 576, 0, -1216, 0, 764, 0, 7036, 0, 5988, 0, 0, 0, 0, 0, -2056, 0, 0, 0, 0, 0, -1080, 0, 1664, 0, 3328, 0, 668, 0, -196, 0, 0, 0, 0, 0, -2368, 0, 0, 0, 0, 0, -2580, 0, -840, 0, -1648, 0, 2892, 0, 2496, 0, 0, 0, 0, 0, 2944, 0, 0, 0, 0, 0, 646, 0, -1180, 0, 2720, 0, 484, 0, -2560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 660, 0, -5164, 0, -64, 0, -704, 0, -2744, 0, 0, 0, 0, 0, -5888, 0, 0, 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, 20, 4, -1, 2, 0]], "char_orbit_index": 8, "prim_orbit_index": 4, "minimal_twist": "160.3.h.a", "char_is_minimal": true, "conrey_index": 159, "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [-2, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [4, 3, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [-2, -2, 1, -2, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [5, -1, -1, -2, 0, -1], [0, 0, 0, 0, 0, 0], [1, 1, -4, 1, -1, -1], [0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 2], [0, 0, 0, 0, 0, 0], [1, -1, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [12, 2, 0, -3, -3, 0], [0, 0, 0, 0, 0, 0], [-5, -6, 4, -2, 2, -1], [0, 0, 0, 0, 0, 0], [-32, -4, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0], [10, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 2, -4, 2, -2, -2], [0, 0, 0, 0, 0, 0], [3, 3, 4, 3, -3, 3], [0, 0, 0, 0, 0, 0], [15, -5, 5, 0, 4, 0], [0, 0, 0, 0, 0, 0], [-1, -1, -8, -1, 1, 2], [0, 0, 0, 0, 0, 0], [4, 4, 6, 4, -4, 0], [0, 0, 0, 0, 0, 0], [-13, -5, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [13, 1, 0, 6, 6, 0], [0, 0, 0, 0, 0, 0], [0, -2, 8, 6, 1, 3], [0, 0, 0, 0, 0, 0], [-42, 8, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [-12, -5, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0], [6, 6, 4, 6, -6, 2], [0, 0, 0, 0, 0, 0], [-8, -8, 8, -8, 8, -3], [0, 0, 0, 0, 0, 0], [55, 11, -9, 7, -3, 1], [0, 0, 0, 0, 0, 0], [-7, -7, -12, -7, 7, 1], [0, 0, 0, 0, 0, 0], [0, 0, -15, 0, 0, -2], [0, 0, 0, 0, 0, 0], [-17, -1, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0], [28, -2, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0], [5, 13, 8, 1, -1, -2], [0, 0, 0, 0, 0, 0], [-47, 13, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0], [-39, -25, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [-6, -6, -2, -6, 6, 2], [0, 0, 0, 0, 0, 0], [-1, -1, 4, -1, 1, 3], [0, 0, 0, 0, 0, 0], [55, 15, 10, 0, -8, 0], [0, 0, 0, 0, 0, 0], [11, 11, -24, 11, -11, -1], [0, 0, 0, 0, 0, 0], [-6, -6, 24, -6, 6, -2], [0, 0, 0, 0, 0, 0], [46, 19, 0, 7, 7, 0], [0, 0, 0, 0, 0, 0], [33, -3, 0, -14, -14, 0], [0, 0, 0, 0, 0, 0], [-5, 11, 16, -13, -3, 1], [0, 0, 0, 0, 0, 0], [-106, -26, 0, 8, 8, 0], [0, 0, 0, 0, 0, 0], [10, -8, 0, -16, -16, 0], [0, 0, 0, 0, 0, 0], [-2, -2, 10, -2, 2, -2], [0, 0, 0, 0, 0, 0], [8, 8, 8, 8, -8, 0], [0, 0, 0, 0, 0, 0], [-5, -25, -15, -5, 1, 5], [0, 0, 0, 0, 0, 0], [5, 5, -12, 5, -5, -1], [0, 0, 0, 0, 0, 0], [-4, -4, -33, -4, 4, -10], [0, 0, 0, 0, 0, 0]]}