# Stored data for newform 338.2.a.e, downloaded from the LMFDB on 24 April 2024.
{"label": "338.2.a.e", "space_label": "338.2.a", "level": 338, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036754, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 59024471494303388, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [0, 1]], [5, [1, 1]]], "qexp_display": "q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-3q^{9}+\\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": "0.019", "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": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "0.061", "prec": 17}, {"__RealLiteral__": 0, "data": "1.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.140", "prec": 17}, {"__RealLiteral__": 0, "data": "4.871", "prec": 17}], "related_objects": ["EllipticCurve/Q/338/e"], "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, 0, -1, 4], "traces": [0, 1, 1, 0, 1, -1, 0, 4, 1, -3, -1, 4, 0, 0, 4, 0, 1, 3, -3, 0, -1, 0, 4, -4, 0, -4, 0, 0, 4, -1, 0, 4, 1, 0, 3, -4, -3, 3, 0, 0, -1, -9, 0, -8, 4, 3, -4, -8, 0, 9, -4, 0, 0, -9, 0, -4, 4, 0, -1, -4, 0, 7, 4, -12, 1, 0, 0, 4, 3, 0, -4, -8, -3, 11, 3, 0, 0, 16, 0, -4, -1, 9, -9, 0, 0, -3, -8, 0, 4, -6, 3, 0, -4, 0, -8, 0, 0, 2, 9, -12, -4, 7, 0, -8, 0, 0, -9, -4, 0, -2, -4, 0, 4, -1, 0, 4, -1, 0, -4, 12, 0, 5, 7, 0, 4, 9, -12, -8, 1, 0, 0, 20, 0, 0, 4, 0, 3, -9, 0, 16, -4, 0, -8, 0, -3, 1, 11, 0, 3, 15, 0, 12, 0, -9, 16, -4, 0, 11, -4, 0, -1, -16, 9, 8, -9, 0, 0, 12, 0, 0, -3, 0, -8, 14, 0, -16, 4, 0, -6, -24, 3, -21, 0, 0, -4, -3, 0, 12, -8, 0, 0, -20, 0, 11, 2, 0, 9, 6, -12, -4, -4, 0, 7, -4, 0, 9, -8, 12, 0, 0, 0, 20, -9, 0, -4, 8, 0, 16, -2, 0, -4, 0, 0, 12, 4, 12, -1, 24, 0, 6, 4, 0, -1, 10, 0, 8, -4, 0, 12, -12, 0, 3, 5, 0, 7, -9, 0, 0, 4, 0, 9, -12, -12, -16, -8, 0, 1, 15, 0, 12, 0, 3, 20, -24, 0, 9, 0, 0, 4, -18, 0, -20, 3, 0, -9, -16, 0, -9, 16, -12, -4, -5, 0, 28, -8, 0, 0, -36, -3, -8, 1, 0, 11, -5, 0, 4, 3, 0, 15, 0, 0, -32, 12, 0, 0, -7, -9, -28, 16, 0, -4, -24, 0, -22, 11, 12, -4, 3, 0, -4, -1, 0, -16, 0, 9, 0, 8, 0, -9, -32, 0, 8, 0, -9, 12, -4, 0, 23, 0, 0, -3, 16, 0, 8, -8, 0, 14, 12, 0, -2, -16, 0, 4, 7, 0, 8, -6, 0, -24, 24, 3, -19, -21, 0, 0, -11, 0, -28, -4, 27, -3, -36, 0, -13, 12, 0, -8, 0, 0, -8, 0, 0, -20, 0, 0, -16, 11, 24, 2, -9, 0, -12, 9, 0, 6, 4, -12, 14, -4, 0, -4, 3, 0, 0, 7, -9, -4, 12, 0, 31, 9, 0, -8, -16, 12, 0, 0, 0, 0, 12, 0, -5, 20, 24, -9, -12, 0, 28, -4, 0, 8, -24, 0, -5, 16, 0, -2, 0, 0, 8, -4, -27, 0, 24, 0, 6, 12, 0, 4, 34, 12, -36, -1, 0, 24, 0, 0, 31, 6, 0, 4, -33, 0, 16, -1, 0, 10, 20, 0, 16, 8, 0, -4, -32, 0, 0, 12, 27, -12, 0, 0, 0, 3, 0, 5, -2, 0, -16, 7, 0, -9, -8, 0, -3, 0, 12, 4, -32, 0, -32, 9, 0, -12, 16, -12, -7, -16, 0, -8, 43, 0, 44, 1, 0, 15, 8, 0, -32, 12, 0, 0, 39, 3, 36, 20, 0, -24, 12, 0, -7, 9, 12, 0, 0, 0, 4, 4, 0, -18, 36, 0, -25, -20, 0, 3, 2, 0, 16, -9, -21, -16, 0, 0, -16, -9, 0, 16, 39, -12, 0, -4, 0, -5, -4, 0, 1, 28, 36, -8, 10, 0, 12, 0, 0, -36, 16, -3, 39, -8, 0, 1, 0, 0, -36, 11, 0, -5, -16, 0, 0, 4, 0, 3, -1, 0, -12, 15, 0, 0, -44, 0, 19, -32, -12, 12, -5, 0, 0, 0, 0, -7, 0, -9, 11, -28, 0, 16, -29, 0, 4, -4, 0, -24, -24, 0, 11, -22, 0, 11, 9, 12, -8, -4, 0, 3, 8, 0, 0, -4, 24, -1, 19, 0, 44, -16, 0, 0, 28, 9, -16, 0, 0, 8, -18, 0, -20, -9, -33, -32, 48, 0, -49, 8, 0, 0, 0, -9, 4, 12, 0, -4, 28, 0, -29, 23, 0, 0, 6, 0, 8, -3, 0, 16, -44, 0, 9, 8, 0, -8, 0, 0, -20, 14, -48, 12, -16, 0, -27, -2, 0, -16, 30, 0, 0, 4, 0, 7, 28, 0, -13, 8, 12, -6, -16, 0, 0, -24, 0, 24, -28, 3, -32, -19, 0, -21, 4, 0, 28, 0, -27, -11, -24, 0, -1, -28, 0, -4, 16, 27, -24, -3, 0, -36, -8, 0, -15, -13, 0, 12, -16, 0, 24, -8, 0, 0, -12, 0, 6, -8, 0, 0, 42, 0, -8, -20, 9, 0, 0, 0, -30, -16, 0, 11, 38, 24, -16, 2, 0, -9, 0, 0, -32, -12, 0, 9, -11, 0, -4, 6, 0, 4, -4, -12, 0, 14, 0, -4, 30, 0, -24, -4, 18, 3, 44, 0, 16, 0, 0, 7, 39, -9, -28, -4, 0, 12, -8, 0, 0, 31, 0, 9, 38, 0, 12, -8, 0, -16, -12, 12, 7, 0, 0, 0, 27, 0, -12, 0, 0, 12, -40, 0, -28, -5, 0, 20, 0, 24, 20, -9, 0, -12, -12, 0, 7, 28, 0, -4, -17, 0, 20, 8, 0, -24, 52, 0, -14, -5, 0, 16, -16, 0, 0, -2, -6, 0, 36, 0, 15, 8, 0, -4, -9, -27, 16, 0, 0, 24, -20, 0, -32, 6, 36, 12, 0, 0, 24, 4, 0, 34, -4, 12, -27, -36, 0, -1, 21, 0, -24, 24, -21, 0, -12, 0, 0, 31, 0, 6, 80, 0, -48, 4, 0, -33, 0, 0, -12, 16, 24, -1, -21, 0, 0, 10, 0, 20, -12, 0, -21, 16, 0, 8, 46, 0, 36, -4, 0, -32, 24, 0, 0, 0, 0, 12, -22, 27, 20, -12, 0, 0, -36, 0, -15, 0, 12, 3, -11, 0, -40, 5, 0, -2, 0, 0, 64, -16, 0, 7, -45, 0, -24, -9, 6, -8, -52, 0, -6, -3, 0, 0, 32, 12, -24, 4, 0, -32, 4, 0, -25, -32, 0, 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.c.a", "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], [-1], [0], [4], [1], [-3], [-1], [4], [0], [0], [4], [0], [1], [3], [-3], [0], [-1], [0], [4], [-4], [0], [-4], [0], [0], [4], [-1], [0], [4], [1], [0], [3], [-4], [-3], [3], [0], [0], [-1], [-9], [0], [-8], [4], [3], [-4], [-8], [0], [9], [-4], [0], [0], [-9], [0], [-4], [4], [0], [-1], [-4], [0], [7], [4], [-12], [1], [0], [0], [4], [3], [0], [-4], [-8], [-3], [11], [3], [0], [0], [16], [0], [-4], [-1], [9], [-9], [0], [0], [-3], [-8], [0], [4], [-6], [3], [0], [-4], [0], [-8], [0], [0], [2], [9], [-12], [-4]]}