# Stored data for newform 786.2.a.g, downloaded from the LMFDB on 19 April 2024.
{"label": "786.2.a.g", "space_label": "786.2.a", "level": 786, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021597797778194, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 768407806440298435, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [2, 1]], [7, [2, 1]], [17, [-7, 1]]], "qexp_display": "q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3144, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 6.276241598872638, "hecke_ring_index": 1, "level_radical": 786, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [786, 1, [263, 133], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 131], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.008", "prec": 17}, {"__RealLiteral__": 0, "data": "1.001", "prec": 17}, {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "2.035", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.183", "prec": 17}], "related_objects": ["EllipticCurve/Q/786/g"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [131, -1]], "trace_display": [-1, 1, -2, -2], "traces": [0, 1, -1, 1, 1, -2, -1, -2, -1, 1, 2, 3, 1, -5, 2, -2, 1, 7, -1, -5, -2, -2, -3, -4, -1, -1, 5, 1, -2, -3, 2, -7, -1, 3, -7, 4, 1, -8, 5, 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1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "786.2.a.g", "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], [-2], [-1], [-2], [-1], [1], [2], [3], [1], [-5], [2], [-2], [1], [7], [-1], [-5], [-2], [-2], [-3], [-4], [-1], [-1], [5], [1], [-2], [-3], [2], [-7], [-1], [3], [-7], [4], [1], [-8], [5], [-5], [2], [-12], [2], [-2], [3], [-2], [4], [8], [1], [-3], [1], [7], [-5], [4], [-1], [-6], [2], [-5], [3], [-3], [-2], [13], [7], [-2], [1], [10], [-3], [8], [7], [-4], [-4], [-16], [-1], [-2], [8], [-1], [-5], [-6], [5], [0], [-2], [1], [12], [6], [-2], [-14], [2], [-3], [-3], [-14], [2], [10], [-4], [-7], [-8], [10], [-1], [12], [3], [3], [-1]]}