# Stored data for newform 390.2.a.b, downloaded from the LMFDB on 02 April 2023.
{"level_primes": [2, 3, 5, 13], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 97768921427943159, "level_radical": 390, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["EllipticCurve/Q/390/b"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 2, "analytic_conductor": 3.114165678829935, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "390.2.a.b", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "390.2.a.b", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.020", "prec": 17}, "traces": [0, 1, -1, -1, 1, 1, 1, -2, -1, 1, -1, 4, -1, -1, 2, -1, 1, 4, -1, -2, 1, 2, -4, 2, 1, 1, 1, -1, -2, 8, 1, 4, -1, -4, -4, -2, 1, 6, 2, 1, -1, 10, -2, 4, 4, 1, -2, 0, -1, -3, -1, -4, -1, 6, 1, 4, 2, 2, -8, 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35, 16, 10, -4, 1, 0, -10, 6, -28, -4, 12, 0, -10, -4, -2, -4, -16, -4, -44, 4, 20, -16, -36, 1, 14, 26, 1, -8, -32, 8, 8, -4, -8, 4, -2, 0, -22, -8, 6, 4, -18, 3, 44, -4, 12, 16, -6, 6, -40, 10, 4, -22, 0, -22, 2, 2, 2, 18, 32, 1, 24, -40, 8, 16, -22, -4, -44, 12, 20, -2, -36, 2, -48, 16, 2, 28, -28, 4, 32, -2, 0, -30, 0, 8, 6, -2, 4, -8, -34, 4, 6, 28, 16, -12, 16, 1, 10, -16, 10, 0, -38, -10, 20, -12, 2, -16, -4, 8, 0, 2, 2, 8, -36, -6, -8, -8, -32, -24, 4, -1, -15, 6, 4, -22, 12, -4, 14, -5, 8, 8, 42, -1, 32, -38, 1, -2, 42, 12, -40, -3, 4, -38, -12, 10, 10, -32, 0, 2, 8, -4, 40, -4, 10, 0, 24, 12, -26, 14, -6, -1], "hecke_ring_index_factorization": [], "nf_label": "1.1.1.1", "field_poly": [0, 1], "atkin_lehner_string": "++-+", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, 1], [3, 1], [5, -1], [13, 1]], "char_values": [390, 1, [131, 157, 301], [1, 1, 1]], "Nk2": 1560, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 2, "trace_display": [-1, -1, 1, -2], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[7, [2, 1]], [11, [-4, 1]], [31, [-4, 1]]], "space_label": "390.2.a", "level": 390, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 1, "hecke_orbit_code": 4503599660925318, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.059", "prec": 17}, {"__RealLiteral__": 0, "data": "1.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.152", "prec": 17}, {"__RealLiteral__": 0, "data": "4.542", "prec": 17}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0], [1], [-1], [-1], [1], [1], [1], [-2], [-1], [1], [-1], [4], [-1], [-1], [2], [-1], [1], [4], [-1], [-2], [1], [2], [-4], [2], [1], [1], [1], [-1], [-2], [8], [1], [4], [-1], [-4], [-4], [-2], [1], [6], [2], [1], [-1], [10], [-2], [4], [4], [1], [-2], [0], [-1], [-3], [-1], [-4], [-1], [6], [1], [4], [2], [2], [-8], [-12], [-1], [-2], [-4], [-2], [1], [-1], [4], [-8], [4], [-2], [2], [0], [-1], [0], [-6], [-1], [-2], [-8], [-1], [-8], [1], [1], [-10], [-12], [2], [4], [-4], [-8], [-4], [-10], [-1], [2], [2], [-4], [0], [-2], [1], [-8], [3], [4], [1]]}