# Stored data for newform 507.2.a.a, downloaded from the LMFDB on 19 April 2024.
{"label": "507.2.a.a", "space_label": "507.2.a", "level": 507, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554939, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1406508242571461818, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 1]], [5, [2, 1]]], "qexp_display": "q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+4q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2028, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 4.0484153824789155, "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": "0.018", "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": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.925", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.763", "prec": 17}], "related_objects": ["EllipticCurve/Q/507/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [13, 1]], "trace_display": [-1, -1, -2, 4], "traces": [0, 1, -1, -1, -1, -2, 1, 4, 3, 1, 2, -4, 1, 0, -4, 2, -1, 2, -1, 0, 2, -4, 4, 0, -3, -1, 0, -1, -4, -10, -2, -4, -5, 4, -2, -8, -1, 2, 0, 0, -6, -6, 4, -12, 4, -2, 0, 0, 1, 9, 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"projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-1], [-1], [-1], [-2], [1], [4], [3], [1], [2], [-4], [1], [0], [-4], [2], [-1], [2], [-1], [0], [2], [-4], [4], [0], [-3], [-1], [0], [-1], [-4], [-10], [-2], [-4], [-5], [4], [-2], [-8], [-1], [2], [0], [0], [-6], [-6], [4], [-12], [4], [-2], [0], [0], [1], [9], [1], [-2], [0], [6], [1], [8], [12], [0], [10], [-12], [-2], [-2], [4], [4], [7], [0], [-4], [8], [-2], [0], [8], [0], [3], [-2], [-2], [1], [0], [-16], [0], [8], [2], [1], [6], [-4], [4], [-4], [12], [10], [-12], [2], [2], [0], [0], [4], [0], [0], [5], [-10], [-9], [-4], [1]]}