# Stored data for newform 39.2.a.a, downloaded from the LMFDB on 24 April 2024.
{"label": "39.2.a.a", "space_label": "39.2.a", "level": 39, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554471, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1907566206816012334, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 1]]], "qexp_display": "q+q^{2}-q^{3}-q^{4}+2q^{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": 156, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 0.3114165678829935, "hecke_ring_index": 1, "level_radical": 39, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [39, 1, [14, 28], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 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": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.925", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.763", "prec": 17}], "related_objects": ["EllipticCurve/Q/39/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [13, -1]], "trace_display": [1, -1, 2, -4], "traces": [0, 1, 1, -1, -1, 2, -1, -4, -3, 1, 2, 4, 1, 1, -4, -2, -1, 2, 1, 0, -2, 4, 4, 0, 3, -1, 1, -1, 4, -10, -2, 4, 5, -4, 2, -8, -1, -2, 0, -1, -6, 6, 4, -12, -4, 2, 0, 0, 1, 9, -1, -2, -1, 6, -1, 8, 12, 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4, 48, -24, 71, -10, 10, 20, 2, 0, -20, -6, -12, -2, 0, 0, 30, 8, 0, -36, -46, -4, -44, 24, 24, 0, 16, -5, 12, 34, 13, 16, 32, 20, -8, 6, 10, 0, 48, 2, -10, 32, 6, -8, 58, 9, -44, -2, -24, -4, -48, -6, 64, -4, 4, -4, 0, 6, 8, 12, 0, 22, -40, 1, 12, 24, -48, 18, -20, -4, 12, 20, -18, -8, -40, 0, 16, 2, 4, 10, -16, -2, -48, 0, 16, -38, 0, -16, 2, 4, 0, -50, 30, -8, 0, 14, 0, 12, 16, -3, 26, 32, 6, 0, -14, 18, 0, -12, 8, -48, -60, 8, 2, 0, -26, 24, -30, 6, 16, 24, 40, -24, -24, -14, -15, -2, 12, -10, 36, 0, -52, -15, 0, 20, -60, 1, -48, 12, 1, 2, -42, -8, -8, -18, -2, -12, 16, 18, 36, -20, 0, 0, 0, 8, 16, 20, 16, 0, 16, 4, -26, -24, 2, 36], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "39.2.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], [2], [-1], [-4], [-3], [1], [2], [4], [1], [1], [-4], [-2], [-1], [2], [1], [0], [-2], [4], [4], [0], [3], [-1], [1], [-1], [4], [-10], [-2], [4], [5], [-4], [2], [-8], [-1], [-2], [0], [-1], [-6], [6], [4], [-12], [-4], [2], [0], [0], [1], [9], [-1], [-2], [-1], [6], [-1], [8], [12], [0], [-10], [12], [2], [-2], [4], [-4], [7], [2], [-4], [-8], [-2], [0], [-8], [0], [-3], [2], [-2], [1], [0], [-16], [-1], [8], [-2], [1], [6], [4], [-4], [4], [-12], [10], [-12], [-2], [2], [-4], [0], [-4], [0], [0], [-5], [10], [9], [4], [1]]}