# Stored data for newform 322.2.a.b, downloaded from the LMFDB on 20 April 2024.
{"label": "322.2.a.b", "space_label": "322.2.a", "level": 322, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925250, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1786364086643228882, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-2, 1]], [5, [0, 1]]], "qexp_display": "q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1288, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 2.571182945085228, "hecke_ring_index": 1, "level_radical": 322, "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": "0.024", "prec": 17}, "analytic_rank_proved": true, "char_values": [322, 1, [185, 281], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 7, 23], "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": "0.972", "prec": 17}, {"__RealLiteral__": 0, "data": "0.048", "prec": 17}, {"__RealLiteral__": 0, "data": "1.930", "prec": 17}, {"__RealLiteral__": 0, "data": "0.192", "prec": 17}, {"__RealLiteral__": 0, "data": "4.867", "prec": 17}], "related_objects": ["EllipticCurve/Q/322/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [7, -1], [23, 1]], "trace_display": [-1, 2, 0, 1], "traces": [0, 1, -1, 2, 1, 0, -2, 1, -1, 1, 0, 4, 2, 0, -1, 0, 1, 6, -1, -6, 0, 2, -4, -1, -2, -5, 0, -4, 1, 10, 0, 4, -1, 8, -6, 0, 1, -2, 6, 0, 0, -10, -2, -4, 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26, -36, 0, 71, 22, 20, 12, 0, -12, 5, -6, 52, 30, 2, -16, -16, 0, 0, -16, 54, 0, 34, 0, -20, -24, 24, 4, 0, -30, 38, 4, -32, 0, 0, 10, -2, -6, 0, -12, -38, -8, 16, 0, 26, -1, -12, 0, 0, 20, -28, 4, 16, 0, -44, 8, -72, -36, 0, -1, 0, 30, 40, -5, -36, 40, -8, 2, 0, -32, -40, -14, -4, 0, 32, -12, -56, 10, 0, -20, 6, 24, -24, 0, -4, 24, 0, 8, 10, -8, -4, -10, 54, 0, -6, 26, 16, 30, 0, 0, -38, 0, 28, 0, 24, 24, 10, -2, 0, 16, 24, -16, 0, -30, 60, -6, 2, 6, 0, 0, 80, -12, 10, 0, -15, 0, 16, -18, 0, 2, -8, -5, -72, 0, -22, -10, 10, 32, 0, 0, 50, 0, -56, 0, -10, -28, 44, 20, 0, -60, 24, 0, 4, 0, 32, -4, -64, 8, 0, -28, -20, -20, 8, 0], "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": "322.2.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], [2], [1], [0], [-2], [1], [-1], [1], [0], [4], [2], [0], [-1], [0], [1], [6], [-1], [-6], [0], [2], [-4], [-1], [-2], [-5], [0], [-4], [1], [10], [0], [4], [-1], [8], [-6], [0], [1], [-2], [6], [0], [0], [-10], [-2], [-4], [4], [0], [1], [12], [2], [1], [5], [12], [0], [-6], [4], [0], [-1], [-12], [-10], [-2], [0], [0], [-4], [1], [1], [0], [-8], [0], [6], [-2], [0], [-8], [-1], [-6], [2], [-10], [-6], [4], [0], [-8], [0], [-11], [10], [-14], [2], [0], [4], [20], [-4], [-14], [0], [0], [-1], [8], [-12], [0], [-2], [-2], [-1], [4], [-5]]}