# Stored data for newform 50.2.a.b, downloaded from the LMFDB on 10 May 2024.
{"label": "50.2.a.b", "space_label": "50.2.a", "level": 50, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660924978, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 977379866071001924, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 1]]], "qexp_display": "q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{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": 200, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 0.39925201010640193, "hecke_ring_index": 1, "level_radical": 10, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [50, 1, [27], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5], "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": "0.995", "prec": 17}, {"__RealLiteral__": 0, "data": "0.071", "prec": 17}, {"__RealLiteral__": 0, "data": "1.955", "prec": 17}, {"__RealLiteral__": 0, "data": "0.197", "prec": 17}, {"__RealLiteral__": 0, "data": "4.760", "prec": 17}], "related_objects": ["EllipticCurve/Q/50/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [5, 1]], "trace_display": [1, -1, 0, -2], "traces": [0, 1, 1, -1, 1, 0, -1, -2, 1, -2, 0, -3, -1, 4, -2, 0, 1, 3, -2, 5, 0, 2, -3, -6, -1, 0, 4, 5, -2, 0, 0, 2, 1, 3, 3, 0, -2, -2, 5, -4, 0, -3, 2, 4, -3, 0, -6, -12, -1, -3, 0, -3, 4, -6, 5, 0, -2, -5, 0, 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0, -6, -18, 24, 5, 0, 19, 8, -4, 30, 0, 52, -10, 4, -30, 0, 11, 28, -40, 6, 0, -18, 6, -41, 12, 0, 9, -12, 2, 4, 0, -3, 4, -60, 0, 0, -2, 24, -15, 0, 0, -18, 9, 8, 9, 0, -2, 28, -12, 36, 0, 12, -5, -27, -17, 0, 20, -24, 15, -10, 0, 17, 12, 48, -6, 0, 4, -8, 0, 30, 0, -15, -6, 18, -12, 0, -8, 13, -26, 26, 0, 12, 2, 18, 0, 0, -12, 48, 10, -44, 0, 12, -6, 39, 12, 0, 0, 0, 30, -6, 0, -27, -8, -6, 17, 0, -12, -32, -2, -15, 0, -3, -16, -10, -2, 0, 2, -57, 11, -45, 0, 20, 12, -6, 3, 0, 0, -24, 20, -24, 0, -58, 2, -17, -24, 0, -9, 28, 20, -10, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "50.2.a.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], [-1], [1], [0], [-1], [-2], [1], [-2], [0], [-3], [-1], [4], [-2], [0], [1], [3], [-2], [5], [0], [2], [-3], [-6], [-1], [0], [4], [5], [-2], [0], [0], [2], [1], [3], [3], [0], [-2], [-2], [5], [-4], [0], [-3], [2], [4], [-3], [0], [-6], [-12], [-1], [-3], [0], [-3], [4], [-6], [5], [0], [-2], [-5], [0], [0], [0], [2], [2], [4], [1], [0], [3], [13], [3], [6], [0], [12], [-2], [-11], [-2], [0], [5], [6], [-4], [-10], [0], [1], [-3], [9], [2], [0], [4], [0], [-3], [15], [0], [-8], [-6], [-2], [-12], [0], [-1], [-2], [-3], [6], [0]]}