# Stored data for newform 507.4.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "507.4.a.d", "space_label": "507.4.a", "level": 507, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220859, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 174824356080917566, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, 1]], [5, [7, 1]]], "qexp_display": "q+q^{2}+3q^{3}-7q^{4}-7q^{5}+3q^{6}+\\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": "0.000", "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": "0.960", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.917", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.801", "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": [1, 3, -7, 10], "traces": [0, 1, 1, 3, -7, -7, 3, 10, -15, 9, -7, 22, -21, 0, 10, -21, 41, 37, 9, -30, 49, 30, 22, -162, -45, -76, 0, 27, -70, -113, -21, -196, 161, 66, 37, -70, -63, -13, -30, 0, 105, -285, 30, 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