# Stored data for newform 786.2.a.k, downloaded from the LMFDB on 19 April 2024.
{"label": "786.2.a.k", "space_label": "786.2.a", "level": 786, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45035996307260178, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 358478528616460898, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-4, 1]], [7, [4, 1]], [17, [2, 1]]], "qexp_display": "q+q^{2}-q^{3}+q^{4}+4q^{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": 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": "0.014", "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": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "0.985", "prec": 17}, {"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "1.963", "prec": 17}, {"__RealLiteral__": 0, "data": "0.162", "prec": 17}, {"__RealLiteral__": 0, "data": "4.931", "prec": 17}], "related_objects": ["EllipticCurve/Q/786/k"], "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, 4, -4], "traces": [0, 1, 1, -1, 1, 4, -1, -4, 1, 1, 4, 0, -1, 6, -4, -4, 1, -2, 1, 4, 4, 4, 0, 4, -1, 11, 6, -1, -4, -6, -4, -2, 1, 0, -2, -16, 1, -8, 4, -6, 4, 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true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "786.2.a.k", "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], [-4], [1], [1], [4], [0], [-1], [6], [-4], [-4], [1], [-2], [1], [4], [4], [4], [0], [4], [-1], [11], [6], [-1], [-4], [-6], [-4], [-2], [1], [0], [-2], [-16], [1], [-8], [4], [-6], [4], [6], [4], [12], [0], [4], [4], [-8], [-1], [9], [11], [2], [6], [12], [-1], [0], [-4], [-4], [-6], [-8], [-4], [-6], [-2], [-4], [1], [24], [0], [-12], [-2], [-4], [-16], [4], [1], [-14], [-8], [-11], [4], [0], [-6], [10], [4], [1], [6], [4], [4], [-8], [12], [6], [0], [10], [4], [-24], [4], [2], [-8], [16], [-1], [6], [9], [0], [11]]}