# Stored data for newform 338.2.a.f, downloaded from the LMFDB on 24 April 2024.
{"label": "338.2.a.f", "space_label": "338.2.a", "level": 338, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170407250, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 180304324693631673, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-1, 1]], [5, [-3, 1]]], "qexp_display": "q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{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": "0.019", "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.985", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.762", "prec": 17}], "related_objects": ["EllipticCurve/Q/338/f"], "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, 1, 3, 1], "traces": [0, 1, 1, 1, 1, 3, 1, 1, 1, -2, 3, -6, 1, 0, 1, 3, 1, -3, -2, -2, 3, 1, -6, 0, 1, 4, 0, -5, 1, 6, 3, 4, 1, -6, -3, 3, -2, 7, -2, 0, 3, 0, 1, -1, -6, -6, 0, -3, 1, -6, 4, 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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], [1], [1], [3], [1], [1], [1], [-2], [3], [-6], [1], [0], [1], [3], [1], [-3], [-2], [-2], [3], [1], [-6], [0], [1], [4], [0], [-5], [1], [6], [3], [4], [1], [-6], [-3], [3], [-2], [7], [-2], [0], [3], [0], [1], [-1], [-6], [-6], [0], [-3], [1], [-6], [4], [-3], [0], [0], [-5], [-18], [1], [-2], [6], [6], [3], [8], [4], [-2], [1], [0], [-6], [-14], [-3], [0], [3], [3], [-2], [-2], [7], [4], [-2], [-6], [0], [8], [3], [1], [0], [-12], [1], [-9], [-1], [6], [-6], [6], [-6], [0], [0], [4], [-3], [-6], [1], [10], [-6], [12], [4]]}