# Stored data for newform 222.2.a.b, downloaded from the LMFDB on 24 April 2024.
{"label": "222.2.a.b", "space_label": "222.2.a", "level": 222, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925150, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1368202346155475166, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-2, 1]], [7, [0, 1]]], "qexp_display": "q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 888, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 1.7726789248724246, "hecke_ring_index": 1, "level_radical": 222, "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": [222, 1, [149, 187], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 37], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.961", "prec": 17}, {"__RealLiteral__": 0, "data": "0.071", "prec": 17}, {"__RealLiteral__": 0, "data": "1.861", "prec": 17}, {"__RealLiteral__": 0, "data": "0.202", "prec": 17}, {"__RealLiteral__": 0, "data": "4.502", "prec": 17}], "related_objects": ["EllipticCurve/Q/222/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1], [37, -1]], "trace_display": [-1, -1, 2, 0], "traces": [0, 1, -1, -1, 1, 2, 1, 0, -1, 1, -2, -4, -1, 6, 0, -2, 1, 6, -1, 8, 2, 0, 4, 0, 1, -1, -6, -1, 0, -6, 2, 4, -1, 4, -6, 0, 1, 1, -8, -6, -2, -6, 0, -8, 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-42, -4, -16, -32, -4, 4, -32, 0, 7, 34, -6, -12, 46, -8, 0, 6, 8, 6, 0, 0, 38, 0, 16, 4, -26, -24, 40, -16, 0, 32, -48, 1, -4, -18, -19, 0, 48, -12, -72, 10, -6, 0, 0, -10, -50, -28, 26, -8, -54, 7, 16, 36, 8, -36, -32, 1, 0, 20, -4, -16, 64, -18, 24, 0, 0, 34, -24, -1, 36, -24, 0, -14, -20, 0, 8, 12, -2, 0, 8, -8, 16, -18, 4, 22, 0, 6, -44, 0, 4, -2, 0, 0, -1, 20, 4, 6, 2, 8, -56, -22, -24, 12, -48, -6, 26, 0, -10, 16, -18, -2, 0, -4, 0, -32, 36, 12, 60, 8, 2, 0, 34, -6, 32, -8, -24, 16, 0, -2, -15, -6, -4, 26, 4, 0, 20, -5, -48, 12, 36, -1, 0, 20, 6, -2, 6, -8, 40, -14, -10, 12, 0, -6, -36, 36, 0, 48, 0, 8, 4, -4, 32, 0, -40, 4, 54, -24, -1, 12], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "222.2.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], [-1], [1], [2], [1], [0], [-1], [1], [-2], [-4], [-1], [6], [0], [-2], [1], [6], [-1], [8], [2], [0], [4], [0], [1], [-1], [-6], [-1], [0], [-6], [2], [4], [-1], [4], [-6], [0], [1], [1], [-8], [-6], [-2], [-6], [0], [-8], [-4], [2], [0], [8], [-1], [-7], [1], [-6], [6], [6], [1], [-8], [0], [-8], [6], [-4], [-2], [-2], [-4], [0], [1], [12], [-4], [-12], [6], [0], [0], [0], [-1], [10], [-1], [1], [8], [0], [6], [-12], [2], [1], [6], [-4], [0], [12], [8], [6], [4], [-10], [-2], [0], [0], [-4], [-8], [16], [1], [-6], [7], [-4], [-1]]}