# Stored data for newform 378.2.g.b, downloaded from the LMFDB on 17 August 2026.
{"Nk2": 1512, "analytic_conductor": 3.0183451964043986, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 3, "char_parity": 1, "char_values": [378, 3, [29, 325], [3, 2]], "cm_discs": [], "conrey_index": 109, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[5, [0, 1]], [11, [36, -6, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504011977785722, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "378.2.g.b", "level": 378, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 7], "level_radical": 42, "minimal_twist": "378.2.g.b", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+(-3+2\\zeta_{6})q^{7}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "378.2.g", "trace_display": [-1, 0, 0, -4], "trace_hash": 691441180056003001, "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 7}, {"__RealLiteral__": 0, "data": "2.015", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "12.190", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "111.004", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.017", "prec": 7}, "traces": [0, 2, -1, 0, -1, 0, 0, -4, 2, 0, 0, 6, 0, 10, 5, 0, -1, 6, 0, 4, 0, 0, -12, 6, 0, 5, -5, 0, -1, -12, 0, 1, -1, 0, -12, 0, 0, 1, 4, 0, 0, 12, 0, -2, 6, 0, 6, -6, 0, 2, -10, 0, -5, -6, 0, 0, -4, 0, 6, -6, 0, 1, -2, 0, 2, 0, 0, 1, 6, 0, 0, -24, 0, -2, 1, 0, -8, 6, 0, 1, 0, 0, -6, -12, 0, 0, 1, 0, 6, 0, 0, -20, -12, 0, -6, 0, 0, 34, -13, 0, 5, 12, 0, 19, 10, 0, 12, 18, 0, -5, 0, 0, 5, -24, 0, 0, 6, 0, 12, 6, 0, -25, 1, 0, 1, 0, 0, -26, -1, 0, 0, -12, 0, -20, -2, 0, 6, -6, 0, -14, 0, 0, 12, 30, 0, 0, 4, 0, -2, -12, 0, -17, 4, 0, 24, 0, 0, 22, 1, 0, 0, -30, 0, -11, -6, 0, 6, 36, 0, 24, 0, 0, 1, 0, 0, 5, -12, 0, 0, 0, 0, -20, 25, 0, 6, 0, 0, -36, 12, 0, 0, 0, 0, 1, -17, 0, 11, 24, 0, -11, 5, 0, -24, 24, 0, 0, 19, 0, -5, 48, 0, -26, -6, 0, 18, 0, 0, 1, 10, 0, 0, 30, 0, 16, -1, 0, 12, -6, 0, -5, 0, 0, -12, 24, 0, 0, -6, 0, 24, -48, 0, -17, -25, 0, -2, 0, 0, 20, 1, 0, 0, -36, 0, 72, 13, 0, -1, -6, 0, -5, 0, 0, -12, 6, 0, 0, 4, 0, 1, 0, 0, 7, -12, 0, 12, -30, 0, -17, 7, 0, 0, -24, 0, 13, 12, 0, -60, -24, 0, -19, 0, 0, -2, -36, 0, 0, 1, 0, -12, 30, 0, 4, 34, 0, 4, 0, 0, 34, -30, 0, 0, -12, 0, 22, -44, 0, -2, 18, 0, -36, 0, 0, 6, 48, 0, 25, -11, 0, 12, 30, 0, -20, 6, 0, -18, 0, 0, 4, -12, 0, 0, -6, 0, 20, -2, 0, 0, -24, 0, -2, 20, 0, 6, -36, 0, 0, 0, 0, 0, 6, 0, 3, 10, 0, -5, 0, 0, 28, 6, 0, 0, -6, 0, -26, -36, 0, -6, -60, 0, -2, 0, 0, 0, 6, 0, 0, -2, 0, -17, -12, 0, 72, 2, 0, -12, 0, 0, 13, 22, 0, -10, -6, 0, 5, 12, 0, -30, 12, 0, -29, 0, 0, -38, -6, 0, 0, -5, 0, -24, 48, 0, 28, 13, 0, -6, -30, 0, -5, -36, 0, 0, -18, 0, -50, 4, 0, -5, -24, 0, -8, 0, 0, -60, -24, 0, 0, -8, 0, -4, 48, 0, 36, 12, 0, 12, 0, 0, 19, -5, 0, 0, -36, 0, 16, 6, 0, 24, 12, 0, 1, 0, 0, -6, -6, 0, 40, -30, 0, 24, 12, 0, 5, 34, 0, 50, 0, 0, 40, 1, 0, 0, 60, 0, -36, 20, 0, -2, 48, 0, 25, 0, 0, 18, -12, 0, 0, -36, 0, 13, 30, 0, -2, 2, 0, -6, 0, 0, -72, 1, 0, 0, 42, 0, -23, 24, 0, -12, -6, 0, -13, 0, 0, 16, 60, 0, 0, 1, 0, 0, -66, 0, 10, 7, 0, 6, 0, 0, -74, -6, 0, -30, -24, 0, -5, 34, 0, 7, 0, 0, -10, 0, 0, 12, -42, 0, 0, -26, 0, -24, -36, 0, 16, 30, 0, 30, 60, 0, -23, -19, 0, 0, 24, 0, 36, -2, 0, 18, 0, 0, 8, 0, 0, 1, 36, 0, 0, 24, 0, 30, 36, 0, 94, -5, 0, -17, 0, 0, 16, -8, 0, 0, -30, 0, -11, -17, 0, 6, 60, 0, 25, 0, 0, 24, 0, 0, -25, 22, 0, 22, 12, 0, -14, 1, 0, 18, 0, 0, 10, 72, 0, 0, 18, 0, -50, 24, 0, -24, -12, 0, 36, -50, 0, 22, -18, 0, 0, -6, 0, -6, 0, 0, -50, -20, 0, -12, 0, 0, -36, -18, 0, 0, 12, 0, -68, -2, 0, -12, 12, 0, -68, 0, 0, -6, 12, 0, 0, 17, 0, 1, -30, 0, -17, 0, 0, 48, 0, 0, 36, 1, 0, -25, -96, 0, -4, 6, 0, 72, 12, 0, -17, 0, 0, 0, 12, 0, 0, 0, 0, 6, 12, 0, -95, -6, 0, 10, -30, 0, 10, -20, 0, 0, -6, 0, -17, -56, 0, -12, -6, 0, 49, 0, 0, -24, -36, 0, 0, -26, 0, 72, -90, 0, 16, -6, 0, 30, 0, 0, 58, 1, 0, 0, 0, 0, -5, 0, 0, 6, -30, 0, -20, 0, 0, 1, -24, 0, -5, 34, 0, 24, 24, 0, -72, -36, 0, -13, 0, 0, 31, -12, 0, 0, 48, 0, 5, 13, 0, -11, 60, 0, -72, 5, 0, -6, 12, 0, 0, -10, 0, 12, -30, 0, -32, 6, 0, -6, 0, 0, -4, 58, 0, 0, 6, 0, 31, 19, 0, -24, 24, 0, -14, 0, 0, 10, -66, 0, 0, -24, 0, -24, -36, 0, 14, -14, 0, 13, 0, 0, 125, 12, 0, -30, -6, 0, -92, 1, 0, 18, -12, 0, -23, 0, 0, 36, 36, 0, 0, 25, 0, -5, 12, 0, 5, -5, 0, 48, 0, 0, 13, -8, 0, 0, -60, 0, -80, 30, 0, -24, -18, 0, 52, 0, 0, -8, 24, 0, 0, 5, 0, -24, -6, 0, 36, -72, 0, -24, 0, 0, 37, -6, 0, 0, 12, 0, -36, 19, 0, 10, 60, 0, 55, 0, 0, 18, -120, 0, 10, -8, 0, 6, 48, 0, 52, -48, 0, 12, 0, 0, -74, 4, 0, 0, 18, 0, 36, 12, 0, 12, 18, 0, -10, -20, 0, 6, 12, 0, 0, 24, 0, -24, -6, 0, 30, 5, 0, -17, 0, 0, 70, -25, 0, 0, -36, 0, 28, -80, 0, 1, 6, 0, 0, 0, 0, -30, -24, 0, 0, 72, 0, -40, -6, 0, -5, 1, 0, -60, 0, 0, -23, 25, 0, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, -1], [0, 0], [-1, 1], [0, 0], [0, 0], [-3, 2], [1, 0], [0, 0], [0, 0], [6, -6], [0, 0], [5, 0], [2, 1], [0, 0], [0, -1], [6, -6], [0, 0], [0, 4], [0, 0], [0, 0], [-6, 0], [0, 6], [0, 0], [5, -5], [0, -5], [0, 0], [1, -3], [-6, 0], [0, 0], [1, -1], [-1, 1], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 1], [4, -4], [0, 0], [0, 0], [6, 0], [0, 0], [-1, 0], [0, 6], [0, 0], [6, -6], [0, -6], [0, 0], [5, -8], [-5, 0], [0, 0], [-5, 5], [-6, 6], [0, 0], [0, 0], [-3, 2], [0, 0], [0, 6], [-6, 6], [0, 0], [0, 1], [-1, 0], [0, 0], [1, 0], [0, 0], [0, 0], [1, -1], [0, 6], [0, 0], [0, 0], [-12, 0], [0, 0], [-2, 2], [1, -1], [0, 0], [-4, 0], [-6, 18], [0, 0], [0, 1], [0, 0], [0, 0], [0, -6], [-6, 0], [0, 0], [0, 0], [0, 1], [0, 0], [6, -6], [0, 0], [0, 0], [-15, 10], [-6, 0], [0, 0], [-6, 6], [0, 0], [0, 0], [17, 0], [-8, 3], [0, 0], [0, 5]]}