# Stored data for newform 507.2.a.e, downloaded from the LMFDB on 16 April 2024.
{"label": "507.2.a.e", "space_label": "507.2.a", "level": 507, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036923, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1158334026167715833, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [5, [-12, 0, 1]]], "qexp_display": "q-q^{3}-2q^{4}+2\\beta q^{5}+\\beta q^{7}+q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2028, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 4.0484153824789155, "hecke_ring_index": 1, "level_radical": 39, "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": "0.518", "prec": 17}, "analytic_rank_proved": true, "char_values": [507, 1, [170, 340], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 13], "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": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "1.885", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.361", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "136.466", "prec": 24}], "related_objects": ["EllipticCurve/2.2.13.1/1521.1/b", "ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1521.1-b"], "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": [0, -2, 0, 0], "traces": [0, 2, 0, -2, -4, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 12, 0, 14, 0, -2, 0, 12, 0, 0, 0, 0, 0, 12, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -8, -8, 0, 0, 0, 24, 0, -24, 0, 0, 0, 0, 0, 2, 0, 0, -16, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -14, 0, -12, 0, -22, 0, 2, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, -24, 0, 0, 24, 0, 0, 0, 0, -28, 36, 0, 2, 0, -12, 0, -12, 4, 0, 0, 0, 0, 12, 0, 0, -24, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -26, 0, -2, 0, 12, 0, 12, 0, 0, 0, 0, 0, 10, -24, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 12, 0, 22, 0, -24, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -4, 12, 0, 0, 0, 0, 0, -24, 0, -28, 0, -2, 0, 0, 0, 0, 0, 0, 0, -36, 16, 0, 0, 0, 16, 0, 0, -14, 0, 0, 0, 0, 0, 48, 0, 12, 0, -24, 0, 26, -48, 0, 0, 0, 0, 6, 0, 0, 48, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 12, 0, 36, 0, -24, 0, 22, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 32, 0, 0, 0, 0, 12, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 20, 0, 0, 0, 0, 0, 22, 0, -24, 0, 24, 0, -34, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 28, 0, 0, -36, 0, 0, 0, 0, 24, -2, 0, 48, 0, 26, 0, 12, 44, 0, 0, 0, 0, 12, 0, 0, -4, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -60, 0, 10, 0, -12, 0, -12, 0, 0, 0, 0, 0, -48, 24, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -14, 0, -2, 0, -12, 0, 34, 48, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, -48, 26, 0, 0, 0, 0, 0, 2, 0, -24, 0, 0, 0, -12, 0, 0, 0, 0, 0, -12, 56, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -4, 12, 0, -96, 0, -10, 0, -24, 24, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -8, 46, 0, 0, 0, 0, 0, -70, 0, -8, 0, 48, 0, 48, 0, 0, 0, 0, 0, -48, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, -12, 0, -12, 0, -30, 0, -22, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -4, -36, 0, 0, 0, 0, 0, -12, 0, 0, 0, -24, 0, -36, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 52, 0, 0, -6, 0, 0, 0, 0, 4, 24, 0, -12, 0, -48, 0, -56, -24, 0, 0, 0, 0, 26, 0, 0, -24, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 28, 0, -108, 0, -38, 0, 2, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 48, 0, 0, 84, 0, 0, 0, 0, 0, 12, 0, 88, 0, 36, 0, 84, -16, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, -16, 12, 0, 0, 0, 0, 0, 0, 0, 14, 0, -60, 0, -52, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -24, -12, 0, 24, 0, -22, 0, 24, -44, 0, 0, 0, 0, -26, 0, 0, 48, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 36, 0, -24, 0, -6, 0, 72, 0, 0, 0, 0, 0, 96, -48, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 2, 0, -14, 0, 96, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -24, -12, 0, 0, 0, 0, 0, -36, 0, 24, 0, 0, 0, 24, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 48, 0, 0, 12, 0, 0, 0, 0, 56, 84, 0, 70, 0, 2, 0, 0, 4, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -16, 0, 24, 0, 24, 0, 68, 0, 0, 0, 0, 0, -54, 72, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 72, 0, -12, -32, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 28, -24, 0, 0, 0, 0, 0, 12, 0, 72, 0, 0, 0, 24, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, -96, 0, 0, -64, 0, 0, 0, 0, -24, -62, 0, -20, 0, 0, 0, -48, 48, 0, 0, 0, 0, 14, 0, 0, -52, 0, 0, 0, 96, -22, 0, 0, 0, 0, 0, 24, 0, -36, 0, 26, 0, -24, 0, 0, 0, 0, 0, 34, -12, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -96, 24, 0, 10, 0, -24, 0, -84, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 88, 0, 36, 0, -24, 0, 96, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, -24, 0, 0, 2, 0, 0, 0, 0, -72, -48, 0, 0, 0, -28, 0, -26, 48, 0, 0, 0, 0, -12, 0, 0, -44, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -56, 0, -12, 0, -108, 0, 0, 0, 0, 0, 72, 4, 0, 0, 0, 8, 0, 0, -48, 0, 0, 0, 0, 0, -96, 0, 12, 0, 12, 0, -32, 0, 0, 0, 0, 0, 70, 0, 0, 0], "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, 13, 2, 1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "39.2.j.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, 0], [1, 0], [0, 0], [-1, 0], [-2, 0], [0, 2], [0, 0], [0, 1], [0, 0], [1, 0], [0, 0], [0, -2], [2, 0], [0, 0], [0, 0], [0, -2], [4, 0], [0, 0], [0, 0], [0, 2], [0, -4], [0, -1], [0, 0], [6, 0], [0, 0], [7, 0], [0, 0], [-1, 0], [0, -2], [6, 0], [0, 0], [0, 1], [0, 0], [0, 2], [0, 0], [6, 0], [-2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [1, 0], [0, 4], [0, 2], [0, 0], [0, -2], [-4, 0], [-4, 0], [0, 0], [0, 0], [0, 0], [12, 0], [0, 0], [-12, 0], [0, 0], [0, -2], [0, 0], [0, 2], [0, 4], [1, 0], [0, 0], [0, 1], [-8, 0], [0, 0], [0, 0], [0, -5], [0, 0], [-6, 0], [0, 0], [0, -6], [0, 0], [0, -1], [0, 0], [-7, 0], [0, -4], [-6, 0], [0, 0], [-11, 0], [0, 8], [1, 0], [0, 0], [0, -8], [0, 2], [0, 0], [0, 0], [-6, 0], [0, 0], [0, 4], [0, 0], [0, 0], [-12, 0], [0, -1], [0, 0], [12, 0], [0, 0], [0, -3], [0, 0], [0, -2], [-14, 0]]}