# Stored data for newform 507.2.e.b, downloaded from the LMFDB on 24 April 2024.
{"label": "507.2.e.b", "space_label": "507.2.e", "level": 507, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538832379, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 186456728074421666, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, -1, 1]], [5, [2, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+(1-\\zeta_{6})q^{3}+\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2028, "analytic_conductor": 4.0484153824789155, "hecke_ring_index": 1, "level_radical": 39, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [507, 3, [170, 340], [3, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 13], "conrey_indexes": [22, 484], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.910", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.512", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "87.304", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 1, -4, -4], "traces": [0, 2, 1, 1, 1, -4, -1, -4, 6, -1, -2, 4, 2, 0, -8, -2, 1, -2, -2, 0, -2, -8, -4, 0, 3, -2, 0, -2, 4, 10, 2, -8, 5, -4, -4, 8, 1, -2, 0, 0, -12, 6, -4, 12, 8, 2, 0, 0, -1, -9, -1, -4, 0, 12, -1, -8, -12, 0, -10, 12, -4, 2, -4, -4, 14, 0, -8, -8, 2, 0, 16, 0, -3, -4, 2, -1, 0, -32, 0, 16, -2, -1, -6, -8, -4, 4, 24, -10, 12, -2, 4, 0, 0, -4, 0, 0, 10, 10, 9, -8, -1, 18, -2, 0, 0, 16, 6, -12, -1, 4, 8, 2, -8, 6, 0, 0, 20, 0, 24, -8, -6, -5, 4, -6, -4, 24, 4, 16, -3, 24, 0, 8, 4, 0, 8, 4, -6, 6, 0, -12, -8, 0, 0, 0, -2, -20, -2, 9, -4, -6, 1, -8, 0, -2, -16, 16, 0, -36, 8, 6, -10, 0, 1, 8, 12, 8, -4, -8, -24, 0, 8, 0, -12, -6, -20, 4, -4, 24, 2, -4, -2, -20, 0, 4, 0, 4, 4, -16, 0, 4, 0, -8, 7, 18, 20, 0, -18, 18, -4, -8, -6, 8, -18, -80, -2, -12, 0, 0, 0, 0, 8, 20, 6, 0, 12, -24, -6, 16, 2, -2, -16, 0, 4, 4, 20, 1, 12, -20, 0, 20, 0, -16, 30, -28, 0, 0, -12, 8, 8, 48, 2, 10, -10, 1, -2, 18, -12, 0, -24, -4, 12, 12, -8, 0, -16, 8, 17, -26, 12, 16, 0, -20, 4, -24, -12, -24, 0, 2, -16, -22, 2, -12, -4, 0, 12, -4, 0, 10, -24, 4, 24, 20, 0, -12, 0, 0, 0, -48, 5, 13, 20, 20, -2, -6, 18, -24, -6, -4, -12, 0, -2, 48, -4, -18, 0, -4, 2, 32, -16, 0, 8, 0, 0, -12, -18, 8, 8, -52, -6, -40, -28, 12, 0, 0, -2, 0, 16, 2, 18, 0, 16, -16, -4, 4, 8, 16, -4, 36, 0, 12, -4, -16, 0, 16, 36, 0, -12, 12, 10, -26, 8, 0, 40, -2, 12, 0, -4, 8, 4, -48, 6, 19, -10, -10, 0, 8, 2, -16, 0, -12, -4, -24, -8, 26, -8, 12, 0, 0, 8, -24, 0, -16, -16, -16, 3, 64, -18, 12, -10, 44, 0, 0, -27, 4, -18, -32, -4, 38, -16, 0, -1, 22, 16, 0, 36, 2, -40, 8, -12, 34, 12, 12, 0, 48, 0, 16, 0, -24, 0, -4, 8, 20, -20, 0, 36, 2, 0, 8, -24, 0, -48, 0, -1, -34, 32, 20, 2, 0, 2, -32, -24, 18, 0, -8, -2, 4, -4, -12, -28, 22, 2, -24, -6, -4, -40, 0, 0, 2, 10, 2, 0, -38, 16, -8, -10, 8, -14, 24, 0, 64, 0, -18, 36, 96, -8, 0, -16, -6, 24, -24, -20, 0, 20, 0, 5, -20, 2, 12, 6, 16, -18, 12, 6, -40, 0, 16, -4, 0, 4, 48, 12, 8, 24, 8, -12, -36, 0, 0, 32, 10, 4, 8, 22, 0, 26, 0, 12, 0, 8, -12, 0, 36, -10, -44, 4, 8, 24, 8, -8, 23, -12, 12, 0, 0, 4, 24, -24, 4, -44, 36, 2, -60, 12, -10, 10, -8, 0, 8, -6, 2, 4, 0, 0, -32, 20, -4, 12, 18, 8, 0, 16, -8, 10, 12, 0, -12, 12, 8, 0, -34, 0, -8, 0, -16, -24, 0, -7, 92, -13, -18, -40, 16, 10, 24, -12, 0, -12, 28, -9, 0, -48, -18, 2, 52, 4, 16, 6, -16, 0, -80, -3, 38, -48, 16, -4, 10, -36, 16, 0, -40, -8, 0, -4, -2, 16, 12, -96, 22, 0, -48, 8, 0, 0, 16, 0, -38, -6, 0, -18, 8, -8, 20, 48, -20, -26, -32, 12, 0, -80, 0, 6, -2, 24, -40, 0, -48, 0, 8, -3, 96, 0, 32, -8, -6, -2, -16, -6, 2, 0, -28, -8, 30, -32, 0, -24, 0, 2, 0, -16, -4, -16, 16, -20, 14, 18, 2, 0, 44, 6, 40, 12, -40, 16, -12, 0, -12, 8, 10, 24, 0, 0, -24, 6, 16, 24, 24, -30, -24, 26, -14, -4, -68, 0, 0, 28, 0, 2, -144, 12, -26, 0, -8, -6, 0, 16, 0, -8, 24, -24, 24, 4, 0, -19, 20, -10, -10, -5, 16, 0, 2, 4, 24, 2, -60, 16, -18, 0, 32, -6, 32, 8, 0, -48, 48, -12, 12, 52, 4, -8, 96, -12, -8, 0, 24, 0, 16, -4, -22, 24, 0, 0, -10, -32, -8, 8, 4, -32, 0, 34, -30, 32, 26, 36, 10, -12, 8, 30, 8, 22, 0, 0, 0, 0, -10, 9, 72, -4, -32, 36, 24, -16, 24, -24, 0, 76, -12, 8, -46, 0, 0, -5, 4, -22, -8, -8, 0, 0, -44, 54, 30, -2, -16, -40, 12, 16, -16, -2, 0, 68, 0, -24, -22, 6, 0, 0, 4, -48, -8, 0, 34, 8, 20, 0, 36, -12, 16, 0, 8, 4, 48, 48, -71, 10, 10, 40, 0, 0, -20, 6, 12, 4, 0, 0, -60, -8, 0, -36, -92, 0, -88, 24, -24, 0, -32, -5, 12, -68, -13, -16, 32, 40, 0, 12, 10, 0, -48, -4, -10, 32, -12, 8, -58, 9, -88, 0, -48, -4, 48, 6, -128, -4, 4, 8, 0, -6, 8, 24, 0, 44, -40, -1, -12, -48, -48, 18, 40, 4, -12, 20, -36, 0, -80, 0, -16, -2, -8, 10, -16, 4, 48, 0, 16, -76, 0, -32, 2, -4, 0, 100, 30, -8, 0, -14, 0, 12, 32, 0, 52, 32, -6, 0, 28, 18, 0, 24, -8, 48, -60, 16, 0, 0, -26, -24, 30, -12, 16, 24, -80, 24, 24, -14, -30, 0, 24, -10, -36, 0, 104, -15, 0, -40, 60, -1, -48, 24, 0, 4, -42, 8, 8, 36, -2, -12, -32, -18, -36, -20, 0, 0, 0, 8, -16, -20, -32, 0, 16, -8, 26, 24, 2, 72], "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, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "39.2.a.a", "char_is_minimal": false, "conrey_index": 22, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [1, -1], [1, -1], [0, 1], [-2, 0], [0, -1], [0, -4], [3, 0], [0, -1], [-2, 2], [4, -4], [1, 0], [0, 0], [-4, 0], [-2, 2], [1, -1], [0, -2], [-1, 0], [0, 0], [0, -2], [-4, 0], [0, -4], [0, 0], [3, -3], [-1, 0], [0, 0], [-1, 0], [4, -4], [10, -10], [0, 2], [-4, 0], [0, 5], [0, -4], [-2, 0], [0, 8], [1, -1], [-2, 2], [0, 0], [0, 0], [-6, 0], [6, -6], [-4, 4], [0, 12], [4, 0], [0, 2], [0, 0], [0, 0], [0, -1], [-9, 9], [-1, 1], [-2, 0], [0, 0], [6, 0], [-1, 1], [-8, 8], [0, -12], [0, 0], [0, -10], [0, 12], [-2, 0], [0, 2], [-4, 4], [-4, 4], [7, 0], [0, 0], [-4, 0], [-8, 8], [2, -2], [0, 0], [8, 0], [0, 0], [0, -3], [-2, 0], [0, 2], [-1, 1], [0, 0], [-16, 0], [0, 0], [8, 0], [-2, 2], [-1, 1], [0, -6], [-4, 0], [0, -4], [0, 4], [12, 0], [0, -10], [12, -12], [-2, 2], [2, 0], [0, 0], [0, 0], [-4, 4], [0, 0], [0, 0], [5, 0], [0, 10], [0, 9], [-4, 0], [0, -1]]}