# Stored data for newform 338.2.c.a, downloaded from the LMFDB on 25 April 2024. {"label": "338.2.c.a", "space_label": "338.2.c", "level": 338, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 137472508242, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2287018307573216130, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 1, 1]], [5, [-3, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}+(-1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "c", "char_is_real": false, "Nk2": 1352, "analytic_conductor": 2.698943588319277, "hecke_ring_index": 1, "level_radical": 26, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.019", "prec": 17}, "analytic_rank_proved": true, "char_values": [338, 3, [171], [2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 13], "conrey_indexes": [191, 315], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.124", "prec": 17}, {"__RealLiteral__": 0, "data": "11.282", "prec": 20}, {"__RealLiteral__": 0, "data": "2.496", "prec": 17}, {"__RealLiteral__": 0, "data": "98.455", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, -1, 6, -1], "traces": [0, 2, -1, -1, -1, 6, -1, -1, 2, 2, -3, 6, 2, 0, 2, -3, -1, 3, -4, 2, -3, 2, 6, 0, -1, 8, 0, -10, -1, -6, -3, 8, -1, 6, -6, -3, 2, -7, -4, 0, 6, 0, -1, 1, -12, 6, 0, -6, -1, 6, -4, -6, 0, 0, 5, 18, -1, -4, -6, -6, 6, -8, -4, 2, 2, 0, -12, 14, 3, 0, 6, -3, 2, -4, -7, -4, 2, -12, 0, 16, -3, -1, 0, -24, -1, 9, -2, -6, 6, -6, -12, 0, 0, -4, 3, 6, 2, -10, 6, 24, -4, 12, 3, -8, 0, 6, 0, -12, 5, 14, 18, -7, 2, 6, 2, 0, 12, 0, 12, 3, -3, -25, 16, 0, -4, -6, 2, -20, -1, -2, 0, -42, 6, 2, 14, -30, 3, 0, 0, 13, -3, 3, 6, 0, -4, -18, 2, 6, 14, -6, -4, -34, 2, -6, 6, 24, 0, 28, -8, 0, -3, 0, -1, -16, 0, 18, 12, 0, 2, 0, -18, -4, 1, 0, 12, -4, 6, 12, -6, -3, 6, 40, 0, 16, 0, -21, -4, 36, 3, 5, -12, 18, -1, -4, 20, 0, -12, 3, -12, -2, 8, 14, 12, 12, 3, 0, 4, 0, 0, 24, -3, 13, 0, 6, -12, 3, -10, -4, -7, 2, -36, 0, 14, -19, -1, 8, -12, 0, 2, 26, 0, 6, -6, -54, 0, -18, -6, -8, 3, -30, -3, -10, 50, -16, -8, 18, 0, 0, 8, 12, 3, -24, -4, 0, -20, -18, -1, -9, 1, 14, 0, -24, 21, 12, 6, 0, 2, -6, -28, -24, 15, 11, -6, 0, 0, 24, 0, 28, -26, 8, -3, 12, 3, 4, -3, -12, 0, 0, 2, 8, -18, 20, 2, 21, -12, -18, -7, -30, 12, 0, 8, 1, 17, 12, -4, -24, -6, -4, 6, 4, -12, -60, 0, -2, -14, 6, -8, 12, 0, 36, 6, -12, 0, -6, 2, 0, 32, -7, 0, 3, -36, 8, 12, -28, 0, 42, -1, 46, 0, -12, 9, 24, -4, -26, 1, 0, 0, -3, -6, -19, 8, 0, -12, 24, -6, -9, 12, 3, -3, 0, 6, 15, -20, 50, 0, -12, -8, -26, 0, 0, -21, 0, 8, 4, -18, 3, -6, 0, -10, 20, 6, -20, -36, 21, -1, -36, -4, -2, -10, -12, 0, 0, 6, 21, 3, 48, -12, -34, 4, 2, -4, 36, -28, 0, -24, -3, -6, 42, -6, 32, 0, 0, 4, -6, 0, -72, 0, -26, -12, -9, -3, -34, 13, -6, 0, 12, -3, -8, 24, 0, -6, -33, 5, 25, 8, -18, -7, 0, 2, -26, 18, 24, 0, 42, -7, -18, -19, 12, -1, 6, -16, 0, 6, 17, 0, 0, -4, -10, -13, -15, 0, 9, 6, 80, -6, -12, 27, 72, 0, -28, 9, -14, -6, 12, -8, 8, -6, 0, 15, -21, 6, 0, 20, 0, -25, -30, 32, -16, -8, 32, 18, 9, 0, -36, 0, 72, -4, -3, 12, 80, 3, 0, 48, 30, 2, 36, 0, 0, 40, -18, 9, 2, 2, -10, -9, -24, 1, -18, -7, 0, 0, -18, 12, -20, 21, 8, 12, 12, -12, 23, 0, 12, -4, 0, 12, -36, 14, -3, 48, -36, 15, -22, 11, -20, 3, 42, 0, 34, 0, 16, 24, -24, 0, -8, -56, -21, 13, 3, -16, 0, 6, -18, -6, -39, -6, 18, 4, 2, -3, -15, 6, 10, 0, -36, 0, 0, 2, -76, 8, -4, 36, 12, -10, 0, -4, 0, -42, 24, 6, 8, 36, 3, -7, -36, -30, 9, -6, 4, 0, 12, -4, 19, 1, 56, 17, -75, -24, -14, 2, -6, 48, 0, 12, 38, 2, 0, -12, -24, 4, 56, -12, 0, 30, 12, 0, -58, 1, -12, -14, -42, 6, 29, 16, 13, -6, -60, 0, 0, -72, 6, -3, 18, 24, 14, 0, -6, -6, 6, -1, -72, 0, 8, -16, 0, -7, -126, 0, -4, -6, 36, 18, -22, -16, 0, -24, 6, 14, 0, 0, -19, 42, -96, -1, 19, -23, -40, 0, 96, 6, -10, 9, 0, 24, 24, 8, 0, 13, -13, -2, 0, 0, 8, 0, -12, 6, 39, -6, 0, -19, 27, -4, 0, 0, -28, 6, 9, 24, -24, -6, 26, 18, 16, -6, 0, -6, 0, 6, 15, 0, -6, -12, 4, 15, 20, -20, -24, -25, -20, 0, 26, 6, -3, -8, -46, -26, 18, 0, -84, 0, 20, 42, 0, 0, -9, -4, -18, -8, -24, -18, 24, 3, 40, 3, 48, 0, -102, 5, 16, 20, 0, 6, -6, 40, -7, 18, -18, -42, 0, 2, 32, 18, -9, 8, -39, -2, 32, -10, -7, 6, 0, 0, -36, 0, 30, 6, 84, 21, -40, -6, 12, -24, 6, 24, 0, 68, 0, -2, 42, -4, -9, -4, -24, 36, -12, 14, 0, 0, 48, 12, 33, -3, -40, -6, 11, -84, -48, 3, -2, -64, 0, 0, -3, 0, -14, -8, 24, -6, -36, 0, -38, 36, -56, 0, 36, 13, 0, -12, -40, -9, 0, 6, -7, 17, -6, -26, 0, 12, -25, 0, 4, -24, 0, -3, 74, -8, -12, -12, -84, 0, -8, 3, 0, -33, 90, 5, 0, -50, 8, -4, 48, 36, 0, 14, 20, 0, 3, -4, -13, -26, -42, 18, -21, -12, 58, 0, 36, -21, 0, -7, 40, -18, 6, 38, -6, -6, -9, 2, 0, -12, -24, 8, 0, 0, 1, 6, 120, 17, 37, 0, 48, 0, 60, 2, -72, -10, 48, -13, 21, 30, 16, 0, 2, -18, 0, -12, -28, -40, -8, 12, 36, -12, 24, 27, 30, -36, 108, 0, -68, 14, 1, 9, 42, -14, 0, 12, 15, -6, 6, 16, 0, -16, -6, 3, -15, 0, 54, 15, -72, -21, 0, -3, -30, 0, -48, -10, -12, 0, 62, -25, -6, 60, 3, -16, 13, 32, 0, 16, -54, -16, 36, -36, 14, 9, -78, 0, 9, 18, -6, 0, 0, -36, -2, -4, -16, -3, -6, -24, 46, -40, 35, -6], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 13, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "26.2.a.a", "char_is_minimal": false, "conrey_index": 191, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, 1], [-1, 1], [0, -1], [3, 0], [0, -1], [0, -1], [1, 0], [0, 2], [-3, 3], [6, -6], [1, 0], [0, 0], [1, 0], [-3, 3], [-1, 1], [0, 3], [-2, 0], [0, 2], [0, -3], [1, 0], [0, 6], [0, 0], [-1, 1], [4, 0], [0, 0], [-5, 0], [-1, 1], [-6, 6], [0, -3], [4, 0], [0, -1], [0, 6], [-3, 0], [0, -3], [2, -2], [-7, 7], [-2, 0], [0, 0], [3, 0], [0, 0], [-1, 1], [0, 1], [-6, 0], [0, 6], [0, 0], [-3, 0], [0, -1], [6, -6], [-4, 4], [-3, 0], [0, 0], [0, 0], [5, -5], [18, -18], [0, -1], [-2, 0], [0, -6], [0, -6], [3, 0], [0, -8], [-4, 4], [2, -2], [1, 0], [0, 0], [-6, 0], [14, -14], [3, -3], [0, 0], [3, 0], [0, -3], [0, 2], [-2, 0], [0, -7], [-4, 4], [2, -2], [-6, 0], [0, 0], [8, 0], [-3, 3], [-1, 1], [0, 0], [-12, 0], [0, -1], [0, 9], [-1, 0], [0, -6], [6, -6], [-6, 6], [-6, 0], [0, 0], [0, 0], [-4, 4], [3, -3], [0, 6], [1, 0], [0, -10], [0, 6], [12, 0], [0, -4]]}