# Stored data for newform 507.4.a.c, downloaded from the LMFDB on 20 April 2024.
{"label": "507.4.a.c", "space_label": "507.4.a", "level": 507, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321850363, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 308073061092858101, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [5, [-12, 1]]], "qexp_display": "q-3q^{3}-8q^{4}+12q^{5}-2q^{7}+9q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8112, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 29.913968372910492, "hecke_ring_index": 1, "level_radical": 39, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [507, 1, [170, 340], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 13], "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": "0.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "1.843", "prec": 17}, {"__RealLiteral__": 0, "data": "0.091", "prec": 17}, {"__RealLiteral__": 0, "data": "4.515", "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], [13, 1]], "trace_display": [0, -3, 12, -2], "traces": [0, 1, 0, -3, -8, 12, 0, -2, 0, 9, 0, 36, 24, 0, 0, -36, 64, -78, 0, -74, -96, 6, 0, -96, 0, 19, 0, -27, 16, 18, 0, 214, 0, -108, 0, -24, -72, 286, 0, 0, 0, 384, 0, 524, -288, 108, 0, 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