# Stored data for newform 338.2.a.a, downloaded from the LMFDB on 12 May 2024.
{"label": "338.2.a.a", "space_label": "338.2.a", "level": 338, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554770, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1205229078904391545, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [3, 1]], [5, [-1, 1]]], "qexp_display": "q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1352, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 2.698943588319277, "hecke_ring_index": 1, "level_radical": 26, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [338, 1, [171], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 13], "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": "0.995", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.973", "prec": 17}], "related_objects": ["EllipticCurve/Q/338/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [13, 1]], "trace_display": [-1, -3, 1, -1], "traces": [0, 1, -1, -3, 1, 1, 3, -1, -1, 6, -1, 2, -3, 0, 1, -3, 1, -3, -6, -6, 1, 3, -2, -4, 3, -4, 0, -9, -1, 2, 3, -4, -1, -6, 3, -1, 6, -3, 6, 0, -1, 0, -3, -5, 2, 6, 4, -13, -3, -6, 4, 9, 0, 12, 9, 2, 1, 18, -2, 10, -3, -8, 4, -6, 1, 0, 6, 2, -3, 12, 1, 5, -6, 10, 3, 12, -6, -2, 0, -4, 1, 9, 0, 0, 3, -3, 5, -6, -2, -6, -6, 0, -4, 12, 13, -6, 3, -14, 6, 12, -4, 4, -9, -8, 0, 3, -12, -4, -9, -19, -2, 9, -1, 2, -18, -4, 2, 0, -10, 3, 3, -7, 8, 0, -4, -9, 6, 16, -1, 15, 0, -1, -6, 6, -2, -9, 3, -12, -12, 7, -1, 39, -5, 0, 6, 2, -10, 18, -3, 18, -12, 9, 6, -18, 2, -4, 0, -10, 4, -36, -1, 4, -9, 4, 0, -6, 0, 0, -3, 0, 3, -36, -5, 20, 6, 4, 2, -30, 6, -9, 6, 0, 0, 24, 4, -3, -12, -6, -13, 9, 6, 10, -3, 16, 14, 0, -6, -9, -12, -10, 4, -6, -4, -2, 9, 0, 8, -24, 0, -12, -3, 23, 12, -15, 4, -5, 9, 4, 19, -30, 2, 0, -9, 21, 1, -24, -2, 24, 18, 15, 4, 6, -2, -11, 0, -13, 10, 12, -3, -9, -3, -18, 7, 0, -8, -6, 0, 0, 4, 0, 9, 0, -6, -8, -16, 9, 1, -15, -15, 3, 0, 12, 1, 12, 6, 12, -6, 18, 2, -24, 9, -13, -3, 0, 12, -8, 12, 12, -7, -24, 1, 26, -39, 4, 5, 18, 0, 0, -6, -8, -2, 42, 10, -7, -18, 10, 3, -18, -18, 0, 12, 5, -9, -12, -6, -8, 18, -14, -2, 24, 4, 18, 0, -1, 10, -6, -4, 18, 36, 4, 1, 12, -4, 18, 9, 0, -4, 57, 0, 13, 6, 4, 0, -18, 0, 2, 3, 23, 0, -6, -3, -8, 36, 13, 5, 12, -20, -9, -6, -7, -4, 0, -2, -4, 30, 5, -6, -9, 9, -24, -6, 17, 0, 21, 0, 10, -24, -10, -4, 0, 3, -12, 12, -4, 6, 27, 13, 0, -9, -16, -6, -48, -10, -27, 3, -2, -16, -30, -14, -30, 0, 12, 6, 3, 9, -4, 12, 22, 10, -18, -4, -24, 6, 0, 4, 9, 2, -6, -9, -4, 0, 36, -8, -10, 24, 0, 0, -21, 12, 21, 3, 5, -23, -78, -12, 12, 15, 8, -4, 0, 5, -33, -9, 7, -4, -6, -19, 24, 30, -22, -2, -36, 0, -39, 9, -6, -21, -54, -1, 26, 24, 0, 2, -27, -24, 0, -18, -10, -15, 27, -4, 21, -6, -16, 2, 12, 11, 20, 0, -2, 13, 30, -10, -10, -12, 24, 3, 72, 9, 3, 3, 0, 18, -12, -7, -14, 0, 16, 8, -12, 6, -5, 0, -6, 0, 12, -4, -5, 0, 32, -9, 0, 0, -14, 6, 4, 8, 0, 16, -34, -9, -10, -1, 54, 15, -8, 15, -26, -3, -60, 0, 39, -12, -36, -1, -12, -12, 12, -6, -7, -12, 60, 6, 0, -18, -4, -2, 27, 24, -12, -9, -17, 13, 0, 3, -19, 0, 37, -12, -48, 8, -12, -12, 4, -12, 9, 7, -33, 24, 0, -1, 18, -26, 11, 39, 2, -4, -9, -5, 31, -18, 33, 0, -30, 0, 16, 6, -18, 8, -48, 2, 0, -42, 24, -10, 0, 7, 28, 18, 24, -10, 27, -3, 22, 18, 3, 18, 30, 0, -2, -12, -35, -5, 12, 9, -7, 12, 6, 6, 6, 8, 0, -18, -26, 14, 0, 2, -16, -24, -4, -4, 36, -18, 6, 0, 11, 1, 36, -10, 9, 6, 5, 4, -69, -18, 16, -36, 0, -4, 30, -1, -2, -12, -14, 4, 15, -18, -38, -9, 20, 0, -12, 4, 24, -57, -1, 0, 60, -13, -12, -6, 10, -4, 0, 0, 6, 18, -8, 0, -63, -2, -16, -3, 37, -23, 36, 0, -36, 6, 14, 3, -72, 8, 44, -36, -12, -13, -45, -5, 0, -12, 8, 20, -12, 9, 7, 6, 0, 7, 33, 4, -12, 0, 18, 2, 39, 4, -4, -30, -38, -5, -24, 6, 16, 9, 0, -9, 27, 24, -22, 6, 8, -17, 54, 0, -8, -21, -14, 0, -27, -10, 15, 24, 43, 10, 18, 4, 4, 0, -12, -3, 0, 12, 47, -12, 18, 4, 0, -6, 4, -27, 24, -13, 0, 0, 9, 9, -12, 16, 24, 6, -6, 48, 19, 10, -18, 27, 0, -3, 0, 2, 45, 16, -11, 30, 16, 14, -9, 30, 0, 0, 10, -12, -18, -6, -10, -3, -32, -9, -36, 4, -2, -12, 0, -22, -36, -10, -42, 18, 39, 4, -36, 24, 20, -6, 4, 0, 72, -4, -9, -9, 28, -2, 39, 6, 4, 9, 30, 4, 0, 0, 25, -36, 54, 8, 24, 10, -30, -24, -38, 0, -36, 0, 18, 21, 0, -12, 36, -21, -56, -3, -25, -5, -78, 23, 0, 78, 7, 12, -12, -12, 12, -15, -49, -8, -36, 4, 46, 0, 20, -5, 0, 33, 11, 9, 20, -7, 24, 4, -8, 6, 0, 19, -84, -24, 9, -30, 39, 22, 21, 2, 21, 36, -47, 0, -30, 39, -8, -9, -16, 6, 18, 21, 78, 54, -9, 1, 0, -26, -8, -24, -36, 0, -15, -2, 0, 27, -9, 24, 24, 0, -54, 18, 0, 10, 24, 15, 1, -27, 24, 4, 42, -21, 0, 6, 12, 16, -48, -2, 36, -12, 36, -11, -54, -20, -6, 0, -42, 2, 3, -13, -25, -30, 0, 10, 9, 10, 18, 12, 0, -24, -54, -3, 23, -72, 10, -9, -12, -3, 12, -3, -15, 0, -24, -18, 16, 12, -23, 7, -54, 14, -15, 0, -7, -16, 0, -8, 30, 12, -12, -6, -114, 5, 31, 0, -9, 6, -39, 0, 20, -12, -30, 4, -12, 5, -10, 0, -10, -32, 27, 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": "26.2.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], [-3], [1], [1], [3], [-1], [-1], [6], [-1], [2], [-3], [0], [1], [-3], [1], [-3], [-6], [-6], [1], [3], [-2], [-4], [3], [-4], [0], [-9], [-1], [2], [3], [-4], [-1], [-6], [3], [-1], [6], [-3], [6], [0], [-1], [0], [-3], [-5], [2], [6], [4], [-13], [-3], [-6], [4], [9], [0], [12], [9], [2], [1], [18], [-2], [10], [-3], [-8], [4], [-6], [1], [0], [6], [2], [-3], [12], [1], [5], [-6], [10], [3], [12], [-6], [-2], [0], [-4], [1], [9], [0], [0], [3], [-3], [5], [-6], [-2], [-6], [-6], [0], [-4], [12], [13], [-6], [3], [-14], [6], [12], [-4]]}