# Stored data for newform 560.2.bj.b, downloaded from the LMFDB on 19 April 2024. {"label": "560.2.bj.b", "space_label": "560.2.bj", "level": 560, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4506004842611248, "dim": 8, "is_polredabs": true, "nf_label": "8.0.11574317056.3", "trace_hash": 1912418381178786917, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [4, 0, 0, 0, 45, 0, 0, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+(\\beta _{2}-\\beta _{6})q^{5}+(-\\beta _{4}+\\beta _{6}+\\cdots)q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "bj", "char_is_real": false, "Nk2": 2240, "analytic_conductor": 4.471622513191702, "hecke_ring_index": 2, "level_radical": 70, "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": "0.630", "prec": 17}, "analytic_rank_proved": true, "char_values": [560, 4, [351, 421, 337, 241], [4, 4, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 5, 7], "conrey_indexes": [97, 433], "field_disc": 11574317056, "field_disc_factorization": [[2, 12], [41, 4]], "field_poly": [4, 0, 0, 0, 45, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.830", "prec": 17}, {"__RealLiteral__": 0, "data": "3.485", "prec": 17}, {"__RealLiteral__": 0, "data": "471.348", "prec": 24}, {"__RealLiteral__": 0, "data": "480.584", "prec": 24}, {"__RealLiteral__": 0, "data": "42624.404", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 2], "traces": [0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 12, 0, 0, 0, -20, 0, 0, 0, 0, 0, -8, 0, -4, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, -4, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -4, 0, 40, 0, 0, 0, -44, 0, 0, 0, 0, 0, -42, 0, 20, 0, -40, 0, 0, 0, -8, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 8, 0, -52, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 32, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, 12, 0, -44, 0, 0, 0, 32, 0, 0, 0, 0, 0, 36, 0, -20, 0, -4, 0, 0, 0, 108, 0, 0, 0, 0, 0, -4, 0, 0, 0, 84, 0, 0, 0, -116, 0, 0, 0, 0, 0, -84, 0, -4, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82, 0, 44, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, -60, 0, 68, 0, 0, 0, -32, 0, 0, 0, 0, 0, -36, 0, 28, 0, -84, 0, 0, 0, -76, 0, 0, 0, 0, 0, 32, 0, 0, 0, 4, 0, 0, 0, 88, 0, 0, 0, 0, 0, -12, 0, 12, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 44, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, -72, 0, -48, 0, 0, 0, 96, 0, 0, 0, 0, 0, 48, 0, 64, 0, 12, 0, 0, 0, -36, 0, 0, 0, 0, 0, -36, 0, 0, 0, 84, 0, 0, 0, -44, 0, 0, 0, 0, 0, 20, 0, 44, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, -48, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, -24, 0, 84, 0, 0, 0, -92, 0, 0, 0, 0, 0, -82, 0, 96, 0, -84, 0, 0, 0, 12, 0, 0, 0, 0, 0, 40, 0, 0, 0, 80, 0, 0, 0, 52, 0, 0, 0, 0, 0, 20, 0, -76, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 20, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 36, 0, 52, 0, 0, 0, -88, 0, 0, 0, 0, 0, -36, 0, -68, 0, -104, 0, 0, 0, 68, 0, 0, 0, 0, 0, 72, 0, 0, 0, 84, 0, 0, 0, -20, 0, 0, 0, 0, 0, -96, 0, -104, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 128, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, -88, 0, 60, 0, 0, 0, 20, 0, 0, 0, 0, 0, 4, 0, -24, 0, -52, 0, 0, 0, -20, 0, 0, 0, 0, 0, 80, 0, 0, 0, 20, 0, 0, 0, -28, 0, 0, 0, 0, 0, -12, 0, -28, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 180, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, -180, 0, 132, 0, 0, 0, 4, 0, 0, 0, 0, 0, -48, 0, 88, 0, -148, 0, 0, 0, 76, 0, 0, 0, 0, 0, 82, 0, 0, 0, 120, 0, 0, 0, 12, 0, 0, 0, 0, 0, -60, 0, 60, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 148, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -108, 0, 56, 0, 0, 0, 68, 0, 0, 0, 0, 0, -4, 0, 0, 0, -148, 0, 0, 0, 84, 0, 0, 0, 0, 0, 4, 0, 0, 0, 232, 0, 0, 0, -140, 0, 0, 0, 0, 0, -272, 0, 40, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, -72, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, -156, 0, 100, 0, 0, 0, -36, 0, 0, 0, 0, 0, -104, 0, 104, 0, -100, 0, 0, 0, -252, 0, 0, 0, 0, 0, 36, 0, 0, 0, -96, 0, 0, 0, 112, 0, 0, 0, 0, 0, 64, 0, -192, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, -8, 0, 0, 0, -76, 0, 0, 0, 0, 0, 28, 0, 60, 0, -44, 0, 0, 0, 120, 0, 0, 0, 0, 0, 4, 0, 0, 0, 152, 0, 0, 0, -92, 0, 0, 0, 0, 0, 44, 0, -88, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 96, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 188, 0, 184, 0, 0, 0, -172, 0, 0, 0, 0, 0, -140, 0, 88, 0, -116, 0, 0, 0, 100, 0, 0, 0, 0, 0, 126, 0, 0, 0, 168, 0, 0, 0, 232, 0, 0, 0, 0, 0, -104, 0, -48, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, 0, 216, 0, 0, 0, 0, 0, -164, 0, 0, 0, 0, 0, 0, 0, 164, 0, -76, 0, 0, 0, 96, 0, 0, 0, 0, 0, -40, 0, -84, 0, 20, 0, 0, 0, 136, 0, 0, 0, 0, 0, 68, 0, 0, 0, -100, 0, 0, 0, -164, 0, 0, 0, 0, 0, -128, 0, -52, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 120, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, -320, 0, 148, 0, 0, 0, -200, 0, 0, 0, 0, 0, -64, 0, -124, 0, -208, 0, 0, 0, 56, 0, 0, 0, 0, 0, 232, 0, 0, 0, -64, 0, 0, 0, -148, 0, 0, 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, 5, 3, -1, 4, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 35, 6, 1, 4, 0]], "char_orbit_index": 36, "prim_orbit_index": 6, "minimal_twist": "140.2.m.a", "char_is_minimal": false, "conrey_index": 97, "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, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 2, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 1, 0, -2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 1, -1, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, -1, 0, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -5, 0, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, -3, -1, 1, 1, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 4, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 5, 2, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, -1, 0, -5, 0, 1, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 4, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -5, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 1, -5, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, -6, 3, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, -4, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -5, 0, 6, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, -5, 2, -4, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -10, -2, 2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0]]}