# Stored data for newform 378.2.a.b, downloaded from the LMFDB on 23 April 2024. {"label": "378.2.a.b", "space_label": "378.2.a", "level": 378, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925306, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 822108664620869282, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [3, 1]], [17, [6, 1]]], "qexp_display": "q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{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": "0.017", "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": "0.984", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.960", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.943", "prec": 17}], "related_objects": ["EllipticCurve/Q/378/b"], "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, -3, 1], "traces": [0, 1, -1, 0, 1, -3, 0, 1, -1, 0, 3, 3, 0, -4, -1, 0, 1, -6, 0, -7, -3, 0, -3, -3, 0, 4, 4, 0, 1, 0, 0, 5, -1, 0, 6, -3, 0, -7, 7, 0, 3, -9, 0, -10, 3, 0, 3, 6, 0, 1, -4, 0, -4, 12, 0, -9, -1, 0, 0, -6, 0, 8, -5, 0, 1, 12, 0, -4, -6, 0, 3, 9, 0, 2, 7, 0, -7, 3, 0, -10, -3, 0, 9, 0, 0, 18, 10, 0, -3, 15, 0, -4, -3, 0, -6, 21, 0, 8, -1, 0, 4, -6, 0, 5, 4, 0, -12, -12, 0, 11, 9, 0, 1, -18, 0, 9, 0, 0, 6, -6, 0, -2, -8, 0, 5, 3, 0, 20, -1, 0, -12, 6, 0, -7, 4, 0, 6, 12, 0, -4, -3, 0, -9, -12, 0, 0, -2, 0, -7, 6, 0, -10, 7, 0, -3, -15, 0, -4, 10, 0, 3, -3, 0, -16, -9, 0, 0, -18, 0, 3, -18, 0, -10, -21, 0, 4, 3, 0, -15, -24, 0, 2, 4, 0, 3, 21, 0, -18, 6, 0, -21, 15, 0, 14, -8, 0, 1, -18, 0, -7, -4, 0, 6, 0, 0, 27, -5, 0, -4, -21, 0, 14, 12, 0, 12, 30, 0, 5, -11, 0, -9, 24, 0, -1, -1, 0, 18, -6, 0, -4, -9, 0, 0, 6, 0, -18, -6, 0, 6, 0, 0, 26, 2, 0, 8, -3, 0, 28, -5, 0, -3, 0, 0, -9, -20, 0, 1, -21, 0, -7, 12, 0, -6, -15, 0, -36, 7, 0, -4, -15, 0, -16, -6, 0, -12, 12, 0, 17, 4, 0, 3, 18, 0, -4, 9, 0, 12, -9, 0, 19, 0, 0, 2, 18, 0, 18, 7, 0, -6, 12, 0, -10, 10, 0, -7, -24, 0, 29, 3, 0, 15, 12, 0, -28, 4, 0, -10, -30, 0, 0, -3, 0, 3, 42, 0, -16, 16, 0, 9, 6, 0, -28, 0, 0, 18, 12, 0, -13, -3, 0, 18, 15, 0, 1, 10, 0, 21, 3, 0, -10, -4, 0, -3, 21, 0, -27, 15, 0, 24, -12, 0, 30, -2, 0, -4, -6, 0, 17, -3, 0, -21, 12, 0, -13, 18, 0, -6, 0, 0, 2, 21, 0, -15, -30, 0, -9, -14, 0, 8, 12, 0, 18, -1, 0, 18, 30, 0, 2, 7, 0, 4, 24, 0, -20, -6, 0, 0, -21, 0, -22, -27, 0, 5, -6, 0, 0, 4, 0, 21, 18, 0, 17, -14, 0, -12, -24, 0, 8, -12, 0, -30, 3, 0, -16, -5, 0, 11, 21, 0, 8, 9, 0, -24, -3, 0, -45, 1, 0, 1, 18, 0, -27, -18, 0, 6, 12, 0, -19, 4, 0, 9, 27, 0, 14, 0, 0, -6, 6, 0, -4, 18, 0, 6, -30, 0, -28, -6, 0, 0, -24, 0, 28, -26, 0, -2, -24, 0, 2, -8, 0, 3, -9, 0, 0, -28, 0, 5, 9, 0, -22, 3, 0, 0, 0, 0, 18, 9, 0, 20, -30, 0, 2, -1, 0, 21, -15, 0, 18, 7, 0, -12, -15, 0, 29, 6, 0, 15, -30, 0, -14, 36, 0, -7, 36, 0, 36, 4, 0, 15, 3, 0, -7, 16, 0, 6, -33, 0, -28, 12, 0, -12, 0, 0, -10, -17, 0, -4, -42, 0, 40, -3, 0, -18, -24, 0, 54, 4, 0, -9, 6, 0, 14, -12, 0, 9, -12, 0, 2, -19, 0, 0, 0, 0, 36, -2, 0, -18, 18, 0, -35, -18, 0, -7, 33, 0, 18, 6, 0, -12, -33, 0, -28, 10, 0, -10, 6, 0, -4, 7, 0, 24, -24, 0, 29, -29, 0, -3, 18, 0, 35, -15, 0, -12, 15, 0, -29, 28, 0, -4, 42, 0, 38, 10, 0, 30, -60, 0, -4, 0, 0, 3, -6, 0, 5, -3, 0, -42, -6, 0, -18, 16, 0, -16, 6, 0, -18, -9, 0, -6, -9, 0, -40, 28, 0, 0, 21, 0, 0, -18, 0, -12, 24, 0, -46, 13, 0, 3, 15, 0, 8, -18, 0, -15, -15, 0, -36, -1, 0, -10, -48, 0, -28, -21, 0, -3, 12, 0, 54, 10, 0, 4, 0, 0, 49, 3, 0, -21, -6, 0, 35, 27, 0, -15, -15, 0, 36, -24, 0, 12, -30, 0, 5, -30, 0, 2, 0, 0, 8, 4, 0, 6, 60, 0, -22, -17, 0, 3, -12, 0, -34, 21, 0, -12, 9, 0, -18, 13, 0, -18, -12, 0, -22, 6, 0, 0, 30, 0, 2, -2, 0, -21, 42, 0, 11, 15, 0, 30, 24, 0, -4, 9, 0, 14, 39, 0, 20, -8, 0, -12, 63, 0, 27, -18, 0, 1, 12, 0, 32, -18, 0, -30, -18, 0, -32, -2, 0, -7, 27, 0, -36, -4, 0, -24, 6, 0, 9, 20, 0, 6, -24, 0, -25, 0, 0, 21, 48, 0, 70, 22, 0, 27, -30, 0, 14, -5, 0, 6, 9, 0, -34, 0, 0, -4, -6, 0, 54, -21, 0, -18, 0, 0, -29, -17, 0, 14, -9, 0, -2, 12, 0, 24, 21, 0, 8, -8, 0, 12, 3, 0, -31, 30, 0, -3, 24, 0, 63, 16, 0, 5, -30, 0, 16, -11, 0, -21, 3, 0, 14, -8, 0, -9, 9, 0, -16, 24, 0, 3, 24, 0, 20, 45, 0, -1, -42, 0, 72, -1, 0, -18, 0, 0, -72, 27, 0, 18, -6, 0, -46, -6, 0, -12, 0, 0, 0, 19, 0, -4, 6, 0, -52, -9, 0, -27, -36, 0, -28, -14, 0, 0, 6, 0, -7, 6, 0, -6, 54, 0, 20, 4, 0, -18, -15, 0, 27, -6, 0, 30, -39, 0, -8, 28, 0, 6, 0, 0, -45, 0, 0, 24, 12, 0, -6, -28, 0, 26, -42, 0, -58, 2, 0, 24, -48, 0, -4, -2, 0, 8, 12, 0, 45, -3, 0, 9, -6, 0, 54, 0, 0, 28, 30, 0, -16, -5, 0, -9, 21, 0, -10, 22, 0, -3], "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.b", "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], [-3], [0], [1], [-1], [0], [3], [3], [0], [-4], [-1], [0], [1], [-6], [0], [-7], [-3], [0], [-3], [-3], [0], [4], [4], [0], [1], [0], [0], [5], [-1], [0], [6], [-3], [0], [-7], [7], [0], [3], [-9], [0], [-10], [3], [0], [3], [6], [0], [1], [-4], [0], [-4], [12], [0], [-9], [-1], [0], [0], [-6], [0], [8], [-5], [0], [1], [12], [0], [-4], [-6], [0], [3], [9], [0], [2], [7], [0], [-7], [3], [0], [-10], [-3], [0], [9], [0], [0], [18], [10], [0], [-3], [15], [0], [-4], [-3], [0], [-6], [21], [0], [8], [-1], [0], [4]]}