# Stored data for newform 507.2.f.e, downloaded from the LMFDB on 25 April 2024.
{"label": "507.2.f.e", "space_label": "507.2.f", "level": 507, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014742140420603, "dim": 8, "is_polredabs": true, "nf_label": "8.0.56070144.2", "trace_hash": 186266550372663344, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [169, 0, 0, 0, 38, 0, 0, 0, 1]], [5, [169, 0, 0, 0, 38, 0, 0, 0, 1]], [7, [2, 2, 1]]], "qexp_display": "q+(\\beta _{1}+\\beta _{2}+\\beta _{4})q^{2}+(\\beta _{4}+\\beta _{5})q^{3}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 39, "char_orbit_label": "f", "char_is_real": false, "Nk2": 2028, "analytic_conductor": 4.0484153824789155, "hecke_ring_index": 4, "level_radical": 39, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.626", "prec": 17}, "analytic_rank_proved": true, "char_values": [507, 4, [170, 340], [2, 3]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 13], "conrey_indexes": [239, 437], "field_disc": 56070144, "field_disc_factorization": [[2, 12], [3, 4], [13, 2]], "field_poly": [13, -38, 70, -74, 63, -34, 16, -4, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "7.425", "prec": 17}, {"__RealLiteral__": 0, "data": "2.236", "prec": 17}, {"__RealLiteral__": 0, "data": "394.752", "prec": 24}, {"__RealLiteral__": 0, "data": "299.580", "prec": 24}, {"__RealLiteral__": 0, "data": "29676.463", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 4, 0, -8], "traces": [0, 8, 0, 4, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 0, -16, 8, 0, -4, -8, 0, -4, -8, 0, -12, 0, 0, 4, 16, 0, 0, -8, 0, -4, 36, 0, 0, 4, 0, 0, -24, 0, 32, 0, 0, -4, 0, 0, 28, 0, 0, 0, 0, 0, 8, -8, 0, -16, 68, 0, -44, -56, 0, 8, 0, 0, -40, -8, 0, 0, 32, 0, 36, 28, 0, 0, 8, 0, 0, 16, 0, -8, 0, 0, -4, 36, 0, 68, 0, 0, 0, 0, 0, 20, -128, 0, -16, -32, 0, -40, -8, 0, 24, 0, 0, 32, -28, 0, 0, 64, 0, -28, -8, 0, 0, 0, 0, 0, 64, 0, 36, 0, 0, 20, -64, 0, 8, 0, 0, 0, 0, 0, -28, 16, 0, 8, 12, 0, 0, 64, 0, -64, 0, 0, 40, 68, 0, 0, -68, 0, 4, -32, 0, 0, 8, 0, 0, -80, 0, -28, 0, 0, -64, -32, 0, -40, 0, 0, 0, 0, 0, -16, 120, 0, 28, -8, 0, 32, 40, 0, 28, 0, 0, -28, 0, 0, 0, -48, 0, -4, -8, 0, 0, -20, 0, 0, 80, 0, -64, 0, 0, 32, 108, 0, -60, 0, 0, 0, 0, 0, 4, -56, 0, 32, 32, 0, 84, 16, 0, -4, 0, 0, -76, -8, 0, 0, 44, 0, -8, 16, 0, 0, 12, 0, 0, -128, 0, 8, 0, 0, 8, -20, 0, -116, 0, 0, 0, 0, 0, -4, 168, 0, -40, 0, 0, 24, -88, 0, 84, 0, 0, 56, -40, 0, 0, -28, 0, 20, -88, 0, 0, 16, 0, 0, 16, 0, 0, 0, 0, 56, 24, 0, -16, 0, 0, 0, 0, 0, -4, -16, 0, 20, -92, 0, 80, 64, 0, -76, 0, 0, 8, -24, 0, 0, -56, 0, -24, 16, 0, 0, -80, 0, 0, 16, 0, 8, 0, 0, 16, 56, 0, 32, 0, 0, 0, 0, 0, 68, -48, 0, -20, -152, 0, -64, -32, 0, -28, 0, 0, 44, -60, 0, 0, -96, 0, 0, -24, 0, 0, 64, 0, 0, -8, 0, 8, 0, 0, 36, -240, 0, 120, 0, 0, 0, 0, 0, 112, 160, 0, 44, -76, 0, 28, -32, 0, 84, 0, 0, -16, -56, 0, 0, 152, 0, -60, 8, 0, 0, -136, 0, 0, 0, 0, -40, 0, 0, 32, 64, 0, 32, 0, 0, 0, 0, 0, -64, -136, 0, 60, 52, 0, 8, 96, 0, 0, 0, 0, 104, 80, 0, 0, 28, 0, -16, -60, 0, 0, 56, 0, 0, 168, 0, -68, 0, 0, 28, 56, 0, -148, 0, 0, 0, 0, 0, 32, 40, 0, -52, 16, 0, 40, 88, 0, 8, 0, 0, -72, -68, 0, 0, 0, 0, 40, -32, 0, 0, -24, 0, 0, 16, 0, -4, 0, 0, -32, 32, 0, 32, 0, 0, 0, 0, 0, 0, -112, 0, -40, 88, 0, 32, 160, 0, 16, 0, 0, -64, 88, 0, 0, -8, 0, -16, -144, 0, 0, 108, 0, 0, -216, 0, -132, 0, 0, 32, 204, 0, -48, 0, 0, 0, 0, 0, -80, -104, 0, -16, 176, 0, -76, -184, 0, 8, 0, 0, -112, 32, 0, 0, -136, 0, 100, -44, 0, 0, 36, 0, 0, 16, 0, 56, 0, 0, 0, -16, 0, -76, 0, 0, 0, 0, 0, -84, 112, 0, 176, 44, 0, 8, 48, 0, -40, 0, 0, 152, -40, 0, 0, 76, 0, 8, 148, 0, 0, 32, 0, 0, -200, 0, -20, 0, 0, -4, -116, 0, 104, 0, 0, 0, 0, 0, 36, 64, 0, 80, 112, 0, -84, 40, 0, -68, 0, 0, 24, 172, 0, 0, 72, 0, 48, 184, 0, 0, -72, 0, 0, 128, 0, 80, 0, 0, -56, -56, 0, 8, 0, 0, 0, 0, 0, 8, -120, 0, -152, -56, 0, 84, -96, 0, -48, 0, 0, -40, 160, 0, 0, -40, 0, -64, 128, 0, 0, 76, 0, 0, 72, 0, 176, 0, 0, -124, -104, 0, 32, 0, 0, 0, 0, 0, -92, 64, 0, -136, -136, 0, -32, 16, 0, 92, 0, 0, 0, -176, 0, 0, -88, 0, -96, -84, 0, 0, 8, 0, 0, 112, 0, -16, 0, 0, -88, 4, 0, -16, 0, 0, 0, 0, 0, 20, -8, 0, -76, 0, 0, -64, -48, 0, -64, 0, 0, -104, -148, 0, 0, 172, 0, 80, 0, 0, 0, -176, 0, 0, 56, 0, 216, 0, 0, -40, 24, 0, 60, 0, 0, 0, 0, 0, 44, -32, 0, 0, -72, 0, -132, -128, 0, -24, 0, 0, 76, 112, 0, 0, 76, 0, -96, -40, 0, 0, -60, 0, 0, 16, 0, 44, 0, 0, -44, -80, 0, 176, 0, 0, 0, 0, 0, 16, 0, 0, -8, -144, 0, -112, -344, 0, 40, 0, 0, -136, -276, 0, 0, -152, 0, 32, 176, 0, 0, -48, 0, 0, 32, 0, -76, 0, 0, -40, -64, 0, 0, 0, 0, 0, 0, 0, -56, -32, 0, -76, -16, 0, -36, -96, 0, 56, 0, 0, 224, 8, 0, 0, 48, 0, 88, 172, 0, 0, 336, 0, 0, 64, 0, -40, 0, 0, 8, -24, 0, 64, 0, 0, 0, 0, 0, 104, 0, 0, 32, 52, 0, -100, -152, 0, 20, 0, 0, 8, 248, 0, 0, 24, 0, -16, 224, 0, 0, -240, 0, 0, 40, 0, 32, 0, 0, 24, 228, 0, 176, 0, 0, 0, 0, 0, -64, -80, 0, 112, 136, 0, 0, 232, 0, -64, 0, 0, 56, -56, 0, 0, 68, 0, 68, 40, 0, 0, 288, 0, 0, -296, 0, 8, 0, 0, 196, 0, 0, -16, 0, 0, 0, 0, 0, -28, -24, 0, 88, 152, 0, 124, 40, 0, -92, 0, 0, -304, -68, 0, 0, 112, 0, -48, -200, 0, 0, -64, 0, 0, -56, 0, 224, 0, 0, 8, -48, 0, -84, 0, 0, 0, 0, 0, 112, -128, 0, -112, -64, 0, 28, -56, 0, 92, 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, 3, 2, -1, 2, 0], [1, 1, 13, 4, -1, 4, 0], [1, 1, 39, 6, 1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "39.2.k.b", "char_is_minimal": true, "conrey_index": 239, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0], [-1, 0, 1, 3, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0], [-2, 0, 0, 2, 0, 1, -1, 0], [-1, 0, 0, -1, 0, 0, 0, 0], [-2, -1, 0, 1, 1, 1, 0, 2], [0, 0, -1, -1, 0, 1, -1, -1], [-1, 0, 1, 5, 0, 1, 0, 0], [1, 0, 0, -1, 0, 0, 0, -2], [-1, -3, -2, -1, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, -2, -1, 0, 0], [-2, 0, 0, 2, 0, 1, -1, 0], [1, 0, -2, 0, 0, 2, 0, 0], [1, 2, 1, 0, 0, -1, -1, 1], [2, -2, -2, -2, -2, -3, -2, 0], [0, 0, 0, 0, 0, -2, 0, 0], [-4, -3, 0, 1, 3, 3, 0, 2], [0, 1, 1, 0, -1, -1, 0, 0], [-1, 0, 3, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -4, -3, -1, -1, 0, 1], [-1, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, -2, -1, -2, -2, -2], [3, 0, 0, -3, 0, -2, 0, 0], [1, 0, -2, 1, -4, -2, 1, 1], [-1, -5, -4, -1, 0, 1, -1, 1], [-3, 0, 0, 3, 0, 4, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0], [-2, -1, 3, 0, 1, 1, 0, -2], [5, 0, -1, 4, 0, 0, 0, 0], [1, 0, -1, 0, -2, -1, 0, 0], [4, 2, -2, -8, 0, -4, 1, -1], [-2, 0, 5, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -4, 0, 0, 4, 0, 0], [-1, -1, -1, 1, -1, 0, 2, 0], [3, 0, 1, 1, 0, -1, 1, 1], [3, 0, -3, -6, 0, -3, 0, 0], [-1, 2, 2, 1, 2, 0, 2, 0], [2, -2, -2, -2, -2, -3, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, 0, 0, 4, 4, 0, 0], [6, 0, -2, -2, -1, 1, -2, -2], [0, 0, 0, -5, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 0, 0, 2], [1, 1, 0, 4, 0, -1, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, 1, 2, 1, 1, 1], [3, 2, 2, -3, 2, -7, 3, 0], [-1, 0, 3, 0, 0, -3, 0, 0], [1, 2, 1, 0, 0, -1, 2, -2], [-2, 0, 0, 2, 0, -2, 2, 0], [9, 0, 0, -9, 0, -1, 0, 0], [2, 2, 0, 0, -2, -2, 0, 0], [-1, 1, -6, -9, -1, -1, 0, -1], [-7, 0, 0, 0, 0, 0, 0, 0], [-3, -6, -3, 0, 0, 3, -4, 4], [-1, 0, 2, 3, 0, 0, 0, 2], [-5, 0, 5, 7, 0, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 3, 3, 2, -1, 3, 3], [-4, 0, 0, 4, 0, 6, 0, 0], [-3, 0, 2, 1, 4, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, -5, 0, -2, 0, 0], [0, -2, -2, 0, -2, 0, 0, 0], [10, 4, -1, 3, -4, -4, 0, -2], [2, 0, 3, 5, 0, 0, 0, 0], [-8, 0, 3, 5, 6, 3, 5, 5], [-1, 0, 1, -1, 0, 1, -1, 1], [0, 0, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, -2, -1, 0, -4, 0], [-3, 0, 6, 0, 4, -2, 0, 0], [-2, 0, 2, -3, 0, 2, 0, 0], [1, 0, 0, -1, 0, 0, -2, 0], [-2, 3, 3, 2, 3, 1, 2, 0], [5, 0, -1, 4, 0, 0, 0, 0], [9, 6, 0, -3, -6, -6, 0, -6], [6, 0, 0, 3, -1, -1, 3, 3], [1, 0, -1, 8, 0, -1, 0, 0], [5, 2, 0, -3, -2, -2, 0, -6], [6, 2, -4, -12, 0, -6, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, -3, -3, -4, -3, 1, -4, 0], [-16, 0, -4, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 2, -2], [-2, 0, 0, 2, 0, 1, -1, 0], [-7, 0, 0, 7, 0, 6, 0, 0], [5, 5, 0, 0, -5, -5, 0, 0], [-9, -2, 4, -3, 2, 2, 0, 0], [-1, 0, -1, 0, 0, 1, 0, 0]]}