# Stored data for newform 160.4.c.b, downloaded from the LMFDB on 20 January 2025. {"Nk2": 2560, "analytic_conductor": 9.440305600918498, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [160, 2, [31, 101, 97], [2, 2, 1]], "cm_discs": [], "conrey_index": 129, "dim": 4, "field_disc": 13456, "field_disc_factorization": [[2, 4], [29, 2]], "field_poly": [49, 0, 15, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [16, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503737133432992, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 256, "hecke_ring_index_factorization": [[2, 8]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 20, 4, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "160.4.c.b", "level": 160, "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": [2, 5], "level_radical": 10, "minimal_twist": "160.4.c.b", "nf_label": "4.0.13456.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{2}q^{3}+(-3+\\beta _{1})q^{5}+\\beta _{2}q^{7}+11q^{9}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "160.4.c", "trace_display": [0, 0, -12, 0], "trace_hash": 2296898339319037954, "trace_moments": [{"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "3.723", "prec": 17}, {"__RealLiteral__": 0, "data": "2.123", "prec": 17}, {"__RealLiteral__": 0, "data": "115.694", "prec": 24}, {"__RealLiteral__": 0, "data": "91.776", "prec": 20}, {"__RealLiteral__": 0, "data": "4555.654", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "traces": [0, 4, 0, 0, 0, -12, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, -428, 0, 0, 0, 632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -680, 0, 0, 0, -132, 0, 0, 0, 1308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 328, 0, 0, 0, -928, 0, 0, 0, -832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1244, 0, 0, 0, 1856, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4056, 0, 0, 0, 192, 0, 0, 0, -8056, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2100, 0, 0, 0, 4068, 0, 0, 0, 5056, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3904, 0, 0, 0, -1896, 0, 0, 0, -10200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -832, 0, 0, 0, 7424, 0, 0, 0, 6932, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6168, 0, 0, 0, -12064, 0, 0, 0, -2432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11072, 0, 0, 0, 2040, 0, 0, 0, 22272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3712, 0, 0, 0, -4708, 0, 0, 0, -7080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6472, 0, 0, 0, -3924, 0, 0, 0, 15040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6952, 0, 0, 0, -21344, 0, 0, 0, -13048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5160, 0, 0, 0, 22272, 0, 0, 0, 12228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5056, 0, 0, 0, -984, 0, 0, 0, 704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28992, 0, 0, 0, 5568, 0, 0, 0, -3904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29696, 0, 0, 0, 2496, 0, 0, 0, -30088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39380, 0, 0, 0, 18560, 0, 0, 0, -7480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44608, 0, 0, 0, 7424, 0, 0, 0, -31896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1672, 0, 0, 0, 3732, 0, 0, 0, 5656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13160, 0, 0, 0, -11136, 0, 0, 0, 14848, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14388, 0, 0, 0, 72, 0, 0, 0, -13832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23224, 0, 0, 0, 29696, 0, 0, 0, -11072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24128, 0, 0, 0, -46400, 0, 0, 0, -3648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5952, 0, 0, 0, -12168, 0, 0, 0, 70008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11496, 0, 0, 0, 6848, 0, 0, 0, 37852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -77320, 0, 0, 0, 24168, 0, 0, 0, 3608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29696, 0, 0, 0, -70528, 0, 0, 0, -41832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15040, 0, 0, 0, -10208, 0, 0, 0, 89088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96216, 0, 0, 0, -6300, 0, 0, 0, -10112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31616, 0, 0, 0, 29092, 0, 0, 0, 48256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -102152, 0, 0, 0, -15168, 0, 0, 0, -111360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46120, 0, 0, 0, 22272, 0, 0, 0, 68544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 79296, 0, 0, 0, 20416, 0, 0, 0, -42688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35768, 0, 0, 0, 11712, 0, 0, 0, 14680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 704, 0, 0, 0, -67624, 0, 0, 0, -79348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44544, 0, 0, 0, 30600, 0, 0, 0, -28992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 111400, 0, 0, 0, 20416, 0, 0, 0, -134200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -163328, 0, 0, 0, 153120, 0, 0, 0, 9664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 2496, 0, 0, 0, 5736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 85288, 0, 0, 0, -44544, 0, 0, 0, 96328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2300, 0, 0, 0, -20796, 0, 0, 0, -11072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10880, 0, 0, 0, 82592, 0, 0, 0, -59392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132744, 0, 0, 0, -111360, 0, 0, 0, -44608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 85376, 0, 0, 0, -18504, 0, 0, 0, 44616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 118976, 0, 0, 0, 72384, 0, 0, 0, 97144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -146888, 0, 0, 0, 7296, 0, 0, 0, 37120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 0, 0, 0, -109504, 0, 0, 0, -89088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88616, 0, 0, 0, -117856, 0, 0, 0, 65728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-3, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [11, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, -3, 1], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, 0, 0, 0], [-16, 0, 0, 0], [0, 0, 0, 0], [0, 0, 13, 0], [0, 0, 0, 0], [-107, -6, 0, 0], [0, 0, 0, 0], [0, 0, 38, 0], [0, 0, 0, 0], [158, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, -3, 1], [0, 0, 0, 0], [0, 26, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-170, 0, 0, 0], [0, 0, 0, 0], [0, 0, -79, 0], [0, 0, 0, 0], [-33, 11, 0, 0], [0, 0, 0, 0], [0, 0, 61, 0], [0, 0, 0, 0], [327, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 46, 0, 0], [0, 0, 0, 0], [0, 0, -116, -3], [0, 0, 0, 0], [0, -48, 0, 0], [0, 0, 0, 0], [0, 0, 0, -15], [0, 0, 0, 0], [82, 0, 0, 0], [0, 0, 0, 0], [0, 0, 11, 0], [0, 0, 0, 0], [-232, -6, 0, 0], [0, 0, 0, 0], [0, 0, 173, 0], [0, 0, 0, 0], [-208, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -22], [0, 0, 0, 0], [0, -40, 0, 0], [0, 0, 0, 0], [0, 0, -107, -6], [0, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, 0, -8], [0, 0, 0, 0], [-311, 0, 0, 0], [0, 0, 0, 0], [0, 0, -235, 0], [0, 0, 0, 0], [464, 12, 0, 0], [0, 0, 0, 0], [0, 0, 158, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, -64, 0, 0], [0, 0, 0, 0], [0, 0, -348, -9], [0, 0, 0, 0], [0, 100, 0, 0], [0, 0, 0, 0], [0, 0, 0, 11], [0, 0, 0, 0]]}