# Stored data for newform 189.2.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "189.2.a.e", "space_label": "189.2.a", "level": 189, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036605, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1284766912762488963, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-3, 0, 1]], [5, [-3, 0, 1]]], "qexp_display": "q+\\beta q^{2}+q^{4}+\\beta q^{5}+q^{7}-\\beta q^{8}+3q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 756, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 1.5091725982021993, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [189, 1, [29, 136], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "1.954", "prec": 17}, {"__RealLiteral__": 0, "data": "0.423", "prec": 17}, {"__RealLiteral__": 0, "data": "15.222", "prec": 20}, {"__RealLiteral__": 0, "data": "5.890", "prec": 17}, {"__RealLiteral__": 0, "data": "149.694", "prec": 24}], "related_objects": ["ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/3969.2/b", "EllipticCurve/2.0.3.1/3969.2/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [7, -1]], "trace_display": [0, 0, 0, 2], "traces": [0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 4, 0, 0, -10, 0, 0, 10, 0, 0, -6, 0, 0, -4, 0, 0, 2, 0, 0, 10, 0, 0, -24, 0, 0, -14, 0, 0, -6, 0, 0, -8, 0, 0, 6, 0, 0, 2, 0, 0, 4, 0, 0, -6, 0, 0, -36, 0, 0, 16, 0, 0, 2, 0, 0, 28, 0, 0, 6, 0, 0, -8, 0, 0, 10, 0, 0, 16, 0, 0, 18, 0, 0, -24, 0, 0, 6, 0, 0, 4, 0, 0, 24, 0, 0, -8, 0, 0, -4, 0, 0, 10, 0, 0, 48, 0, 0, -14, 0, 0, -10, 0, 0, 6, 0, 0, -24, 0, 0, -16, 0, 0, 10, 0, 0, -20, 0, 0, 12, 0, 0, 10, 0, 0, 24, 0, 0, 40, 0, 0, 18, 0, 0, -36, 0, 0, -14, 0, 0, -20, 0, 0, -6, 0, 0, -20, 0, 0, -18, 0, 0, 4, 0, 0, -36, 0, 0, -18, 0, 0, -8, 0, 0, -4, 0, 0, -30, 0, 0, 4, 0, 0, -6, 0, 0, 24, 0, 0, 30, 0, 0, -44, 0, 0, 2, 0, 0, -50, 0, 0, 48, 0, 0, 18, 0, 0, -20, 0, 0, 4, 0, 0, -12, 0, 0, 10, 0, 0, -6, 0, 0, -38, 0, 0, 36, 0, 0, -8, 0, 0, 36, 0, 0, 24, 0, 0, -24, 0, 0, 16, 0, 0, 16, 0, 0, 20, 0, 0, -42, 0, 0, -6, 0, 0, 38, 0, 0, -14, 0, 0, 24, 0, 0, 48, 0, 0, 28, 0, 0, 40, 0, 0, 12, 0, 0, -38, 0, 0, -6, 0, 0, -8, 0, 0, -12, 0, 0, 62, 0, 0, -8, 0, 0, -24, 0, 0, -12, 0, 0, -8, 0, 0, -50, 0, 0, 34, 0, 0, 30, 0, 0, 4, 0, 0, 16, 0, 0, 36, 0, 0, 6, 0, 0, -8, 0, 0, -18, 0, 0, 40, 0, 0, -36, 0, 0, -26, 0, 0, -24, 0, 0, 2, 0, 0, 6, 0, 0, 28, 0, 0, 18, 0, 0, 18, 0, 0, 12, 0, 0, 12, 0, 0, 4, 0, 0, -50, 0, 0, -42, 0, 0, -38, 0, 0, -24, 0, 0, 16, 0, 0, -30, 0, 0, -6, 0, 0, -8, 0, 0, -24, 0, 0, -36, 0, 0, 4, 0, 0, 20, 0, 0, 20, 0, 0, -36, 0, 0, -8, 0, 0, 10, 0, 0, -36, 0, 0, -30, 0, 0, 34, 0, 0, -48, 0, 0, 16, 0, 0, -24, 0, 0, 52, 0, 0, -14, 0, 0, -32, 0, 0, -48, 0, 0, -30, 0, 0, 2, 0, 0, -18, 0, 0, 12, 0, 0, 34, 0, 0, 6, 0, 0, -44, 0, 0, 60, 0, 0, 28, 0, 0, 24, 0, 0, -20, 0, 0, -36, 0, 0, -28, 0, 0, -16, 0, 0, -8, 0, 0, 6, 0, 0, 144, 0, 0, -50, 0, 0, 64, 0, 0, 72, 0, 0, 48, 0, 0, -20, 0, 0, -8, 0, 0, 6, 0, 0, -24, 0, 0, -12, 0, 0, 22, 0, 0, 30, 0, 0, -40, 0, 0, 10, 0, 0, -12, 0, 0, 66, 0, 0, -62, 0, 0, 72, 0, 0, -80, 0, 0, 12, 0, 0, 16, 0, 0, 40, 0, 0, -16, 0, 0, 0, 0, 0, 36, 0, 0, -18, 0, 0, 52, 0, 0, 18, 0, 0, 4, 0, 0, -36, 0, 0, -48, 0, 0, 0, 0, 0, 50, 0, 0, 70, 0, 0, -24, 0, 0, 12, 0, 0, 28, 0, 0, -20, 0, 0, -56, 0, 0, 48, 0, 0, 22, 0, 0, 6, 0, 0, 34, 0, 0, 12, 0, 0, -22, 0, 0, -20, 0, 0, 16, 0, 0, 24, 0, 0, 4, 0, 0, 42, 0, 0, -86, 0, 0, -120, 0, 0, 24, 0, 0, 4, 0, 0, 24, 0, 0, 24, 0, 0, -20, 0, 0, 36, 0, 0, -36, 0, 0, 84, 0, 0, -20, 0, 0, -18, 0, 0, -8, 0, 0, -30, 0, 0, 12, 0, 0, 40, 0, 0, 16, 0, 0, -114, 0, 0, -72, 0, 0, -4, 0, 0, -70, 0, 0, -114, 0, 0, -38, 0, 0, 30, 0, 0, -12, 0, 0, 60, 0, 0, 10, 0, 0, 4, 0, 0, -80, 0, 0, -24, 0, 0, 64, 0, 0, -18, 0, 0, 76, 0, 0, 48, 0, 0, -12, 0, 0, 24, 0, 0, -56, 0, 0, -72, 0, 0, -20, 0, 0, -30, 0, 0, -14, 0, 0, 132, 0, 0, -44, 0, 0, -44, 0, 0, -20, 0, 0, -24, 0, 0, -18, 0, 0, -10, 0, 0, -8, 0, 0, 48, 0, 0, 32, 0, 0, -50, 0, 0, -96, 0, 0, -12, 0, 0, 6, 0, 0, -48, 0, 0, -86, 0, 0, 42, 0, 0, -40, 0, 0, 18, 0, 0, 28, 0, 0, -24, 0, 0, 64, 0, 0, 4, 0, 0, -36, 0, 0, 108, 0, 0, 158, 0, 0, 4, 0, 0, -16, 0, 0, 48, 0, 0, 88, 0, 0, 12, 0, 0, 82, 0, 0, -78, 0, 0, 6, 0, 0, 10, 0, 0, 56, 0, 0, 30, 0, 0, -44, 0, 0, 30, 0, 0, 112, 0, 0, -66, 0, 0, -20, 0, 0, -38, 0, 0, 12, 0, 0, 36, 0, 0, -192, 0, 0, -36, 0, 0, -20, 0, 0, 12, 0, 0, 36, 0, 0, -8, 0, 0, -32, 0, 0, 126, 0, 0, 28, 0, 0, 108, 0, 0, 10, 0, 0, -48, 0, 0, 88, 0, 0, 24, 0, 0, 18, 0, 0, 24, 0, 0, -16, 0, 0, 24, 0, 0, -30, 0, 0, -96, 0, 0, -12, 0, 0, 16, 0, 0, 4, 0, 0, -24, 0, 0, 40, 0, 0, -80, 0, 0, 30, 0, 0, 126, 0, 0, -36, 0, 0, 20, 0, 0, 4, 0, 0, 18, 0, 0, 52, 0, 0, 42], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "189.2.a.e", "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, 0], [1, 0], [0, 1], [0, 0], [1, 0], [0, 1], [0, 0], [1, 0], [0, -1], [0, 0], [3, 0], [0, -1], [0, 0], [2, 0], [0, 1], [0, 0], [-5, 0], [0, -4], [0, 0], [5, 0], [0, 1], [0, 0], [-3, 0], [0, 1], [0, 0], [-2, 0], [0, 2], [0, 0], [1, 0], [0, -6], [0, 0], [5, 0], [0, -3], [0, 0], [-12, 0], [0, 1], [0, 0], [-7, 0], [0, 5], [0, 0], [-3, 0], [0, 3], [0, 0], [-4, 0], [0, -1], [0, 0], [3, 0], [0, 4], [0, 0], [1, 0], [0, -2], [0, 0], [2, 0], [0, 8], [0, 0], [-3, 0], [0, -1], [0, 0], [-18, 0], [0, -4], [0, 0], [8, 0], [0, 5], [0, 0], [1, 0], [0, 2], [0, 0], [14, 0], [0, -4], [0, 0], [3, 0], [0, 3], [0, 0], [-4, 0], [0, -7], [0, 0], [5, 0], [0, -1], [0, 0], [8, 0], [0, -5], [0, 0], [9, 0], [0, -6], [0, 0], [-12, 0], [0, -4], [0, 0], [3, 0], [0, -5], [0, 0], [2, 0], [0, 1], [0, 0], [12, 0], [0, 5], [0, 0], [-4, 0], [0, 1], [0, 0], [-2, 0]]}