# Stored data for newform 6040.2.a.p, downloaded from the LMFDB on 19 April 2024.
{"label": "6040.2.a.p", "space_label": "6040.2.a", "level": 6040, "weight": 2, "hecke_orbit": 16, "hecke_orbit_code": 67553994444117912, "dim": 19, "is_polredabs": true, "trace_hash": 840610812197999206, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [5628, -40224, 59750, 91643, -206783, -80919, 262172, 41499, -174105, -17345, 67665, 6652, -15895, -1891, 2208, 325, -165, -29, 5, 1]], [7, [-1728, 35712, 241472, -294336, -1635684, 664688, 2923099, -718804, -2052760, 290672, 680951, -37587, -116773, -1504, 10488, 660, -465, -46, 8, 1]], [11, [-71561024, -609210640, -476487589, 671346706, 732532046, -179591575, -376254655, -34467342, 82896806, 22378192, -7442617, -3458077, 134882, 231329, 18635, -6616, -1110, 38, 18, 1]]], "qexp_display": "q-\\beta _{1}q^{3}+q^{5}+\\beta _{3}q^{7}+(1+\\beta _{1}+\\beta _{2}+\\cdots)q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 24160, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 48.22964282085335, "hecke_ring_index": 128, "level_radical": 1510, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [6040, 1, [1511, 3021, 2417, 761], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 5, 151], "conrey_indexes": [1], "field_disc": 46075205295344840596518165697457888256, "field_disc_factorization": [[2, 10], [3, 2], [3271, 1], [1528425478828601375557500974521, 1]], "field_poly": [-5628, -40224, -59750, 91643, 206783, -80919, -262172, 41499, 174105, -17345, -67665, 6652, 15895, -1891, -2208, 325, 165, -29, -5, 1], "hecke_ring_index_factorization": [[2, 7]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.788", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "617.886", "prec": 24}, {"__RealLiteral__": 0, "data": "303.066", "prec": 24}, {"__RealLiteral__": 0, "data": "41115.262", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 19, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1], [151, -1]], "trace_display": [0, -5, 19, -8], "traces": [0, 19, 0, -5, 0, 19, 0, -8, 0, 26, 0, -18, 0, 5, 0, -5, 0, -4, 0, -27, 0, -18, 0, -25, 0, 19, 0, -35, 0, -35, 0, -26, 0, 0, 0, -8, 0, -10, 0, -48, 0, -14, 0, -21, 0, 26, 0, -40, 0, 23, 0, -32, 0, -3, 0, -18, 0, -13, 0, -28, 0, -46, 0, -53, 0, 5, 0, -42, 0, -31, 0, -46, 0, 31, 0, -5, 0, 15, 0, -56, 0, 31, 0, -25, 0, -4, 0, -20, 0, -7, 0, -61, 0, 29, 0, -27, 0, 39, 0, -52, 0, -39, 0, -13, 0, -18, 0, -28, 0, -16, 0, -19, 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