# Stored data for newform 65.2.a.a, downloaded from the LMFDB on 19 April 2024.
{"label": "65.2.a.a", "space_label": "65.2.a", "level": 65, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554497, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1364169308829084149, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]]], "qexp_display": "q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{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": 260, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 0.5190276131383225, "hecke_ring_index": 1, "level_radical": 65, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [65, 1, [27, 41], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [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": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.965", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.794", "prec": 17}], "related_objects": ["EllipticCurve/Q/65/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [13, 1]], "trace_display": [-1, -2, -1, -4], "traces": [0, 1, -1, -2, -1, -1, 2, -4, 3, 1, 1, 2, 2, -1, 4, 2, -1, 2, -1, -6, 1, 8, -2, -6, -6, 1, 1, 4, 4, 2, -2, -10, -5, -4, -2, 4, -1, -2, 6, 2, -3, -6, -8, 10, -2, -1, 6, 4, 2, 9, -1, -4, 1, 2, -4, -2, 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"prim_orbit_index": 1, "minimal_twist": "65.2.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], [-2], [-1], [-1], [2], [-4], [3], [1], [1], [2], [2], [-1], [4], [2], [-1], [2], [-1], [-6], [1], [8], [-2], [-6], [-6], [1], [1], [4], [4], [2], [-2], [-10], [-5], [-4], [-2], [4], [-1], [-2], [6], [2], [-3], [-6], [-8], [10], [-2], [-1], [6], [4], [2], [9], [-1], [-4], [1], [2], [-4], [-2], [-12], [12], [-2], [6], [-2], [2], [10], [-4], [7], [1], [4], [-4], [-2], [12], [-4], [6], [3], [-6], [2], [-2], [6], [-8], [-2], [-12], [1], [-11], [6], [-16], [-8], [-2], [-10], [-4], [6], [2], [1], [4], [6], [20], [-4], [6], [10], [-2], [-9], [2], [-1]]}