# Stored data for newform 503.2.a.a, downloaded from the LMFDB on 24 April 2024.
{"label": "503.2.a.a", "space_label": "503.2.a", "level": 503, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554935, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 751317792920231628, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]], [3, [-1, 1]]], "qexp_display": "q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}-3q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2012, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 4.016475221670404, "hecke_ring_index": 1, "level_radical": 503, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [503, 1, [5], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [503], "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": "0.954", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.861", "prec": 17}, {"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "4.565", "prec": 17}], "related_objects": ["EllipticCurve/Q/503/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[503, -1]], "trace_display": [-1, 1, -4, -3], "traces": [0, 1, -1, 1, -1, -4, -1, -3, 3, -2, 4, 5, -1, 1, 3, -4, -1, 0, 2, 8, 4, -3, -5, 9, 3, 11, -1, -5, 3, -6, 4, -2, -5, 5, 0, 12, 2, 2, -8, 1, -12, -10, 3, 5, -5, 8, -9, -1, -1, 2, -11, 0, -1, -6, 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"inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "503.2.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "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], [-4], [-1], [-3], [3], [-2], [4], [5], [-1], [1], [3], [-4], [-1], [0], [2], [8], [4], [-3], [-5], [9], [3], [11], [-1], [-5], [3], [-6], [4], [-2], [-5], [5], [0], [12], [2], [2], [-8], [1], [-12], [-10], [3], [5], [-5], [8], [-9], [-1], [-1], [2], [-11], [0], [-1], [-6], [5], [-20], [-9], [8], [6], [4], [4], [5], [2], [6], [7], [-4], [-5], [13], [0], [9], [-12], [6], [-6], [6], [-2], [11], [-8], [-15], [-1], [16], [4], [1], [10], [9], [3], [0], [-5], [-6], [15], [-6], [-8], [-3], [-9], [-2], [1], [-32], [-5], [10], [-2], [-10], [-11]]}