# Stored data for newform 378.2.a.a, downloaded from the LMFDB on 02 April 2023.
{"level_primes": [2, 3, 7], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 1732093336220366515, "level_radical": 42, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["EllipticCurve/Q/378/a"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 3.0183451964043986, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "378.2.a.a", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "378.2.a.a", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.010", "prec": 17}, "traces": [0, 1, -1, 0, 1, -4, 0, -1, -1, 0, 4, 4, 0, 3, 1, 0, 1, 7, 0, 2, -4, 0, -4, 1, 0, 11, -3, 0, -1, -1, 0, -9, -1, 0, -7, 4, 0, 2, -2, 0, 4, -6, 0, 11, 4, 0, -1, 6, 0, 1, -11, 0, 3, 9, 0, -16, 1, 0, 1, 5, 0, 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-16, -15, 0, -19, 21, 0, 26, 12, 0, 0, 12, 0, 8, 12, 0, -48, 1, 0, 4, 9, 0, 63, 24, 0, -8, 36, 0, 12, 9, 0, -12, 48, 0, 16, 29, 0, -14, 1, 0, 22, 4, 0, -14, 21, 0, 22, -22, 0, 1, 30, 0, 2, 4, 0, -8, -112, 0, -52, 7, 0, -24, 2, 0, -6, 5, 0, -44, 2, 0, -42, -22, 0, 7, -8, 0, 48, -12, 0, 8, 22, 0, 50, -6, 0, -10, -20, 0, -40, -5, 0, -32, 15, 0, -10, -26, 0, -6, 42, 0, 12, -4, 0, 24, -36, 0, 104, 7, 0, 6, 11, 0, 26, 9, 0, 7, 28, 0, 35, -28, 0, 24], "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], [7, 1]], "char_values": [378, 1, [29, 325], [1, 1]], "Nk2": 1512, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 2, "trace_display": [-1, 0, -4, -1], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [4, 1]], [17, [-7, 1]]], "space_label": "378.2.a", "level": 378, "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": 33554810, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.034", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.090", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.250", "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], [0], [1], [-4], [0], [-1], [-1], [0], [4], [4], [0], [3], [1], [0], [1], [7], [0], [2], [-4], [0], [-4], [1], [0], [11], [-3], [0], [-1], [-1], [0], [-9], [-1], [0], [-7], [4], [0], [2], [-2], [0], [4], [-6], [0], [11], [4], [0], [-1], [6], [0], [1], [-11], [0], [3], [9], [0], [-16], [1], [0], [1], [5], [0], [-6], [9], [0], [1], [-12], [0], [7], [7], [0], [-4], [7], [0], [-14], [-2], [0], [2], [-4], [0], [-6], [-4], [0], [6], [4], [0], [-28], [-11], [0], [-4], [3], [0], [-3], [1], [0], [-6], [-8], [0], [-8], [-1], [0], [11]]}