# Stored data for newform 222.2.a.e, downloaded from the LMFDB on 04 June 2023.
{"level_primes": [2, 3, 37], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 262859999510976781, "level_radical": 222, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["EllipticCurve/Q/222/e"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 5, "analytic_conductor": 1.7726789248724246, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "222.2.a.e", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "222.2.a.e", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 1, 1, 1, 1, 0, 1, -1, 1, 1, 0, 3, 1, -1, -1, 0, 1, -3, 1, -7, 0, -1, 3, 3, 1, -5, -1, 1, -1, 0, 0, 2, 1, 3, -3, 0, 1, 1, -7, -1, 0, -6, -1, -4, 3, 0, 3, 6, 1, -6, -5, -3, -1, 9, 1, 0, -1, -7, 0, 0, 0, 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0, 0, -6, -25, 3, 0, 36, 18, 1, -5, 0, 3, -16, -42, -18, 0, -1, -3, -18, 0, -5, -27, -18, 4, -6, 0, 5, 23, -24, 6, 0, 24, -7, 9, 8, 0, -16, -18, -3, 38, 0, -16, -6, -12, -3, -5, -34, 14, 0, 18, 0, 42, 30, 0, 6, 0, -1, 38, -2, -10, 0, -6, 8, -18, 0, 0, -12, 6, 2, -5, 35, 30, 3, -24, 9, 0, -24, 0, -39, 12, 0, -27, -1, 9, -28, 0, -3, 44, -2, 21, 0, -12, 1, -14, 38, 5, -10, -3, 11, -9, 0, 5, 15, -18, -6, 0, 0, -6, 7, -12, 0, -16, 2, -4, -12, 0, 3, 53, -13, 1, 0], "hecke_ring_index_factorization": [], "nf_label": "1.1.1.1", "field_poly": [0, 1], "atkin_lehner_string": "---", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [37, -1]], "char_values": [222, 1, [149, 187], [1, 1]], "Nk2": 888, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 2, "trace_display": [1, 1, 0, -1], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [0, 1]], [7, [1, 1]]], "space_label": "222.2.a", "level": 222, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 1, "hecke_orbit_code": 18014398543036638, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.011", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.079", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.366", "prec": 17}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0], [1], [1], [1], [1], [0], [1], [-1], [1], [1], [0], [3], [1], [-1], [-1], [0], [1], [-3], [1], [-7], [0], [-1], [3], [3], [1], [-5], [-1], [1], [-1], [0], [0], [2], [1], [3], [-3], [0], [1], [1], [-7], [-1], [0], [-6], [-1], [-4], [3], [0], [3], [6], [1], [-6], [-5], [-3], [-1], [9], [1], [0], [-1], [-7], [0], [0], [0], [-10], [2], [-1], [1], [0], [3], [2], [-3], [3], [0], [12], [1], [5], [1], [-5], [-7], [-3], [-1], [2], [0], [1], [-6], [3], [-1], [0], [-4], [0], [3], [-3], [0], [1], [3], [2], [6], [0], [1], [2], [-6], [3], [-5]]}