# Stored data for newform 405.4.a.a, downloaded from the LMFDB on 19 April 2024.
{"label": "405.4.a.a", "space_label": "405.4.a", "level": 405, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67109269, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1456597096200777130, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [5, 1]]], "qexp_display": "q-5q^{2}+17q^{4}+5q^{5}+9q^{7}-45q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6480, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 23.89577355232495, "hecke_ring_index": 1, "level_radical": 15, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [405, 1, [326, 82], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.965", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.894", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.682", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1]], "trace_display": [-5, 0, 5, 9], "traces": [0, 1, -5, 0, 17, 5, 0, 9, -45, 0, -25, -8, 0, 43, -45, 0, 89, -122, 0, -59, 85, 0, 40, -213, 0, 25, -215, 0, 153, 224, 0, -36, -85, 0, 610, 45, 0, 206, 295, 0, -225, 413, 0, -392, -136, 0, 1065, -311, 0, -262, -125, 0, 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