# Stored data for newform 378.2.a.c, downloaded from the LMFDB on 25 April 2024.
{"label": "378.2.a.c", "space_label": "378.2.a", "level": 378, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007199288295802, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 686417491481491251, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [1, 1]], [17, [2, 1]]], "qexp_display": "q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1512, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 3.0183451964043986, "hecke_ring_index": 1, "level_radical": 42, "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": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [378, 1, [29, 325], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "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": "0.960", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.853", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.477", "prec": 17}], "related_objects": ["EllipticCurve/Q/378/c"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1], [7, 1]], "trace_display": [-1, 0, -1, -1], "traces": [0, 1, -1, 0, 1, -1, 0, -1, -1, 0, 1, -5, 0, 0, 1, 0, 1, -2, 0, -1, -1, 0, 5, 1, 0, -4, 0, 0, -1, -4, 0, -9, -1, 0, 2, 1, 0, 5, 1, 0, 1, 9, 0, -10, -5, 0, -1, -6, 0, 1, 4, 0, 0, -12, 0, 5, 1, 0, 4, 14, 0, 0, 9, 0, 1, 0, 0, -8, -2, 0, -1, 13, 0, -2, -5, 0, -1, 5, 0, 6, -1, 0, -9, 4, 0, 2, 10, 0, 5, 9, 0, 0, 1, 0, 6, 1, 0, 16, -1, 0, -4, 14, 0, -1, 0, 0, 12, -12, 0, 7, -5, 0, -1, 2, 0, -1, -4, 0, -14, 2, 0, 14, 0, 0, -9, 9, 0, 0, -1, 0, 0, -22, 0, 1, 8, 0, 2, -16, 0, -20, 1, 0, -13, 0, 0, 4, 2, 0, 5, -6, 0, 10, 1, 0, -5, 9, 0, 8, -6, 0, 1, -1, 0, -4, 9, 0, -4, -10, 0, -13, -2, 0, -10, -7, 0, 4, -5, 0, -9, -24, 0, 18, 0, 0, -1, -5, 0, 10, -6, 0, -1, 3, 0, -10, -16, 0, 1, 10, 0, -13, 4, 0, -14, 4, 0, -9, 1, 0, 0, 5, 0, -22, -12, 0, 12, 10, 0, 9, -7, 0, 5, 0, 0, 5, 1, 0, -2, -6, 0, 28, 1, 0, 4, -14, 0, 6, 14, 0, -2, -24, 0, 14, -14, 0, 0, -1, 0, 0, 9, 0, -9, 24, 0, -5, 0, 0, 1, -27, 0, -5, 0, 0, 22, 21, 0, 12, -1, 0, -8, -13, 0, 24, -2, 0, 16, 20, 0, -19, 20, 0, -1, 10, 0, -20, 13, 0, 0, -9, 0, -13, -4, 0, -2, -18, 0, -14, -5, 0, 6, 0, 0, 10, -10, 0, -1, 0, 0, -5, 5, 0, -9, 8, 0, -8, -8, 0, 6, 18, 0, 20, -1, 0, 1, 2, 0, 0, 4, 0, -9, 6, 0, -4, 4, 0, 10, 8, 0, 27, 13, 0, 2, 45, 0, -1, 10, 0, 7, 3, 0, -26, -4, 0, 5, 3, 0, -13, 9, 0, 24, -4, 0, -18, -18, 0, 0, 2, 0, 35, 1, 0, 5, 12, 0, -17, -10, 0, 6, 0, 0, -14, 1, 0, -3, 10, 0, -5, 10, 0, 16, 20, 0, -2, -1, 0, -10, -6, 0, -30, 13, 0, -4, 12, 0, 0, 14, 0, -4, -25, 0, -10, 9, 0, -1, -14, 0, -4, 0, 0, -5, -6, 0, -27, 22, 0, 12, 8, 0, 0, -12, 0, -10, 15, 0, -4, -9, 0, 7, -1, 0, 24, -5, 0, 0, -11, 0, -9, -5, 0, -1, -10, 0, -45, 2, 0, 6, 0, 0, 13, -28, 0, -1, -31, 0, -14, -4, 0, 14, 26, 0, 8, -6, 0, -14, 50, 0, 4, 2, 0, 24, -32, 0, 0, -14, 0, 14, -16, 0, 26, 0, 0, 1, -9, 0, 8, 0, 0, -9, -13, 0, 10, 9, 0, -24, -36, 0, -14, 5, 0, 0, -18, 0, 2, -1, 0, 27, 1, 0, 30, 5, 0, 0, 15, 0, 11, -22, 0, -21, 18, 0, -22, -12, 0, 1, 0, 0, 12, 8, 0, 13, -5, 0, -3, -24, 0, 2, -7, 0, 12, -16, 0, -20, 4, 0, -6, 19, 0, -20, -22, 0, 0, 1, 0, -10, 4, 0, -2, 20, 0, -13, -30, 0, 18, 0, 0, 9, -4, 0, -14, 13, 0, 4, -4, 0, 60, 2, 0, 18, -14, 0, 9, 14, 0, 5, -9, 0, -2, -6, 0, 0, 27, 0, 8, -10, 0, 10, -14, 0, 12, 1, 0, 0, 0, 0, -15, 5, 0, -5, -14, 0, -11, 9, 0, -8, -9, 0, 11, 8, 0, 8, -10, 0, 38, -6, 0, -18, 0, 0, 0, -20, 0, 1, 22, 0, -13, -1, 0, -2, -42, 0, -70, 0, 0, -4, 30, 0, 22, 9, 0, -6, -17, 0, 28, 4, 0, -4, -1, 0, -4, -10, 0, -8, 0, 0, 26, -27, 0, -13, -27, 0, -16, -2, 0, -45, 9, 0, 16, 1, 0, -10, 0, 0, -4, -7, 0, -3, 20, 0, -18, 26, 0, 4, 20, 0, -5, -5, 0, -3, -14, 0, -25, 13, 0, -9, -9, 0, 0, -24, 0, 4, 30, 0, 1, 18, 0, 18, 16, 0, -32, 0, 0, -2, 20, 0, -18, -35, 0, -1, 40, 0, 18, -5, 0, -12, 21, 0, 6, 17, 0, 10, 12, 0, 18, -6, 0, 0, -10, 0, 42, 14, 0, -1, 22, 0, -7, 3, 0, -10, 0, 0, 40, 5, 0, -10, -19, 0, 36, -16, 0, -20, -9, 0, -65, 2, 0, 1, -8, 0, 0, 10, 0, 6, -2, 0, 0, 30, 0, -13, 33, 0, 12, 4, 0, -12, 10, 0, 1, 0, 0, -14, 20, 0, 1, 4, 0, 25, 4, 0, 10, 10, 0, -9, 10, 0, 34, 1, 0, 14, 33, 0, 10, 4, 0, 0, -2, 0, 10, 5, 0, 6, 4, 0, -13, 27, 0, -22, 13, 0, -14, -12, 0, -8, 5, 0, -16, 0, 0, 12, -3, 0, -25, 10, 0, -15, -16, 0, 7, 4, 0, 9, -30, 0, 0, -7, 0, 1, -9, 0, -50, -24, 0, 5, 15, 0, 32, 0, 0, 11, -36, 0, 0, 9, 0, 5, 6, 0, 24, 1, 0, 10, 36, 0, 24, 45, 0, -2, -18, 0, 30, -6, 0, 0, 24, 0, -20, -13, 0, 28, 22, 0, 4, 1, 0, 31, 0, 0, -20, 14, 0, 4, 42, 0, -1, -14, 0, -26, -10, 0, -28, -8, 0, 6, -13, 0, 9, 14, 0, -50, 17, 0, 0, -4, 0, -2, -44, 0, -3, -24, 0, 32, 16, 0, 50, 0, 0, 14, 10, 0, 2, -14, 0, 16, -36, 0, 20, -26, 0, 0, -60, 0, -45, -1, 0, 9, 30, 0, -10, -8, 0, 0, -10, 0, -4, 9, 0, 13, 13, 0, 38, -10, 0, -9], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "378.2.a.c", "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], [0], [1], [-1], [0], [-1], [-1], [0], [1], [-5], [0], [0], [1], [0], [1], [-2], [0], [-1], [-1], [0], [5], [1], [0], [-4], [0], [0], [-1], [-4], [0], [-9], [-1], [0], [2], [1], [0], [5], [1], [0], [1], [9], [0], [-10], [-5], [0], [-1], [-6], [0], [1], [4], [0], [0], [-12], [0], [5], [1], [0], [4], [14], [0], [0], [9], [0], [1], [0], [0], [-8], [-2], [0], [-1], [13], [0], [-2], [-5], [0], [-1], [5], [0], [6], [-1], [0], [-9], [4], [0], [2], [10], [0], [5], [9], [0], [0], [1], [0], [6], [1], [0], [16], [-1], [0], [-4]]}