# Stored data for newform 650.2.a.f, downloaded from the LMFDB on 16 April 2024.
{"label": "650.2.a.f", "space_label": "650.2.a", "level": 650, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170407562, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 814983760467091829, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [-2, 1]], [7, [5, 1]]], "qexp_display": "q-q^{2}+2q^{3}+q^{4}-2q^{6}-5q^{7}-q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2600, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 5.190276131383225, "hecke_ring_index": 1, "level_radical": 130, "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": "0.021", "prec": 17}, "analytic_rank_proved": true, "char_values": [650, 1, [27, 301], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5, 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": "0.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.955", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.883", "prec": 17}], "related_objects": ["EllipticCurve/Q/650/f"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, 1], [13, 1]], "trace_display": [-1, 2, 0, -5], "traces": [0, 1, -1, 2, 1, 0, -2, -5, -1, 1, 0, -3, 2, -1, 5, 0, 1, -3, -1, -4, 0, -10, 3, -6, -2, 0, 1, -4, -5, 9, 0, 5, -1, -6, 3, 0, 1, -2, 4, -2, 0, 0, 10, -2, 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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], [2], [1], [0], [-2], [-5], [-1], [1], [0], [-3], [2], [-1], [5], [0], [1], [-3], [-1], [-4], [0], [-10], [3], [-6], [-2], [0], [1], [-4], [-5], [9], [0], [5], [-1], [-6], [3], [0], [1], [-2], [4], [-2], [0], [0], [10], [-2], [-3], [0], [6], [9], [2], [18], [0], [-6], [-1], [9], [4], [0], [5], [-8], [-9], [-9], [0], [-1], [-5], [-5], [1], [0], [6], [-5], [-3], [-12], [0], [0], [-1], [-14], [2], [0], [-4], [15], [2], [-16], [0], [-11], [0], [15], [-10], [0], [2], [18], [3], [-6], [0], [5], [-6], [10], [-9], [0], [-2], [-8], [-18], [-3], [0]]}