# Stored data for newform 39.2.a.b, downloaded from the LMFDB on 20 April 2024.
{"label": "39.2.a.b", "space_label": "39.2.a", "level": 39, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660924967, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 1437883122427244167, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 2, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}+q^{3}+(1-2\\beta )q^{4}-2\\beta q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 156, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 0.3114165678829935, "hecke_ring_index": 1, "level_radical": 39, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "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": "0.025", "prec": 17}, "analytic_rank_proved": true, "char_values": [39, 1, [14, 28], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 13], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "1.887", "prec": 17}, {"__RealLiteral__": 0, "data": "0.090", "prec": 17}, {"__RealLiteral__": 0, "data": "8.929", "prec": 17}, {"__RealLiteral__": 0, "data": "1.541", "prec": 17}, {"__RealLiteral__": 0, "data": "58.986", "prec": 20}], "related_objects": ["Genus2Curve/Q/1521/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [13, 1]], "trace_display": [-2, 2, 0, 0], "traces": [0, 2, -2, 2, 2, 0, -2, 0, -6, 2, -8, -4, 2, -2, 8, 0, 6, 4, -2, 0, 16, 0, 4, -8, -6, 6, 2, 2, -16, 4, -8, -8, 6, -4, 12, -16, 2, -4, -8, -2, -8, 16, 8, 8, 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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": "39.2.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, 0], [1, 0], [-1, 1], [1, 0], [1, -2], [0, -2], [-1, 1], [0, 2], [-3, 1], [1, 0], [-4, 2], [-2, 0], [1, -2], [-1, 0], [4, -2], [0, -2], [3, 0], [2, 4], [-1, 1], [0, -2], [8, -2], [0, 2], [2, -2], [-4, 0], [-3, 1], [3, 0], [1, -1], [1, 0], [-8, 2], [2, 0], [-4, 2], [-4, 2], [3, 1], [-2, 0], [6, -2], [-8, 0], [1, -2], [-2, -4], [-4, 2], [-1, 0], [-4, 6], [8, -2], [4, -2], [4, -4], [-2, 4], [0, -2], [4, -4], [-6, -4], [3, 0], [1, 0], [-3, 3], [2, 4], [-1, 2], [-2, 0], [-1, 1], [0, 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