# Stored data for newform 1170.2.bs.c, downloaded from the LMFDB on 19 April 2024.
{"label": "1170.2.bs.c", "space_label": "1170.2.bs", "level": 1170, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9010222945272978, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 856089455971570223, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [81, 0, -9, 0, 1]], [11, [81, 0, -9, 0, 1]]], "qexp_display": "q+(\\zeta_{12}-\\zeta_{12}^{3})q^{2}+(1-\\zeta_{12}^{2})q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "bs", "char_is_real": false, "Nk2": 4680, "analytic_conductor": 9.342497036489805, "hecke_ring_index": 1, "level_radical": 390, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.196", "prec": 17}, "analytic_rank_proved": true, "char_values": [1170, 6, [911, 937, 1081], [6, 6, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 13], "conrey_indexes": [361, 901], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "3.742", "prec": 17}, {"__RealLiteral__": 0, "data": "0.725", "prec": 17}, {"__RealLiteral__": 0, "data": "53.097", "prec": 20}, {"__RealLiteral__": 0, "data": "17.753", "prec": 20}, {"__RealLiteral__": 0, "data": "1151.443", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 14, 12, 0, -2, 6, 0, -12, 0, 0, -6, 12, 0, -4, 0, 0, 0, -12, 0, 0, 0, 0, 0, 6, 0, 18, 12, 0, -4, 36, 0, -4, 0, 0, 12, 0, 0, 4, 0, 0, 10, 12, 0, 6, 6, 0, 12, -36, 0, -2, -6, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, -12, 0, -12, -36, 0, 4, 0, 0, 0, 0, 0, -18, 0, 0, 6, 18, 0, 0, 24, 0, 6, 6, 0, 42, 0, 0, -2, 18, 0, -16, 0, 0, -12, 18, 0, 0, 0, 0, 0, 0, 0, 12, -24, 0, 0, 54, 0, -4, 0, 0, -6, 0, 0, -32, 0, 0, -4, 24, 0, 18, 0, 0, -18, -18, 0, 8, -6, 0, 24, 0, 0, 12, -6, 0, 0, 0, 0, 0, 6, 0, 0, -12, 0, -52, -18, 0, -2, 0, 0, -6, 0, 0, -6, 0, 0, 46, -12, 0, 4, -30, 0, 0, 0, 0, -24, -12, 0, -4, 42, 0, 12, 12, 0, 0, 0, 0, 0, -42, 0, -36, -12, 0, 8, -54, 0, -8, 0, 0, 6, 0, 0, 0, -18, 0, -4, -36, 0, 4, 6, 0, 30, 0, 0, 18, 24, 0, 12, 30, 0, -12, -6, 0, 0, -36, 0, 0, 12, 0, 12, -12, 0, 12, -36, 0, 18, 0, 0, -30, 0, 0, 2, 0, 0, -36, -12, 0, 2, 24, 0, -36, 18, 0, -2, 0, 0, -72, 0, 0, -42, -24, 0, 0, -36, 0, 0, -30, 0, 12, -12, 0, 12, 0, 0, 2, 0, 0, 0, 0, 0, 40, 0, 0, -30, 0, 0, -38, -12, 0, -30, -18, 0, 0, 12, 0, -24, 24, 0, 0, 30, 0, 0, 18, 0, 0, -18, 0, -6, -12, 0, 64, 0, 0, 2, 0, 0, -36, 0, 0, 36, 18, 0, -14, -36, 0, 0, -18, 0, 24, -18, 0, -6, 0, 0, 4, 0, 0, -18, 18, 0, 0, 0, 0, 0, -54, 0, -66, -12, 0, 12, 18, 0, 12, 0, 0, -12, 0, 0, 4, 54, 0, 0, -12, 0, 32, 12, 0, -18, -36, 0, -20, 18, 0, 12, -24, 0, 72, -6, 0, 0, -36, 0, 0, -12, 0, 42, -84, 0, 144, 0, 0, -12, 0, 0, -18, 0, 0, 2, 18, 0, 6, 36, 0, -36, 36, 0, 6, -36, 0, -8, 0, 0, -12, 0, 0, 36, 0, 0, 0, 54, 0, 0, -6, 0, -54, 36, 0, 8, 18, 0, 4, 0, 0, -12, 0, 0, 38, 0, 0, 18, 48, 0, 24, -6, 0, 0, -54, 0, 0, 0, 0, -24, 30, 0, -30, 6, 0, 0, 54, 0, 0, -12, 0, -6, 96, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -6, 90, 0, 72, 0, 0, 4, -6, 0, -84, 18, 0, 4, 24, 0, 0, 42, 0, -6, 36, 0, 0, 0, 0, 0, -36, 0, 6, -72, 0, -64, 36, 0, 18, 0, 0, -48, 0, 0, -18, 54, 0, -14, -12, 0, -16, 12, 0, 54, -72, 0, -50, -6, 0, 36, 144, 0, 30, 0, 0, 0, 0, 0, 0, 12, 0, -18, 48, 0, 56, -18, 0, 6, 0, 0, -54, 0, 0, -8, -18, 0, -20, -12, 0, 0, 36, 0, -24, -36, 0, 12, -6, 0, -8, 0, 0, 108, -12, 0, 0, -108, 0, 0, 18, 0, 36, -12, 0, -24, 0, 0, 6, 0, 0, -18, 0, 0, -18, 0, 0, 36, 24, 0, 34, -12, 0, 30, 0, 0, 44, -6, 0, 4, 0, 0, 114, 48, 0, 0, 0, 0, 0, -6, 0, 42, -144, 0, 4, 36, 0, -26, 0, 0, -72, 0, 0, -36, 18, 0, 8, 72, 0, 2, 78, 0, -6, 36, 0, -18, -12, 0, 0, 0, 0, -6, -18, 0, 0, -36, 0, 0, 24, 0, 114, 24, 0, -12, -36, 0, 48, 0, 0, 0, 0, 0, -28, 18, 0, 44, 48, 0, -18, -6, 0, 18, -108, 0, 6, -30, 0, 8, 42, 0, -96, 30, 0, 0, 18, 0, 0, 30, 0, 0, -12, 0, -144, 0, 0, -30, 0, 0, 90, 0, 0, 24, 72, 0, 12, -24, 0, 24, 24, 0, -54, -72, 0, -2, 12, 0, -8, 30, 0, -30, 12, 0, 0, -36, 0, 0, 0, 0, 144, 24, 0, 36, -36, 0, -12, 0, 0, 54, 0, 0, 20, 0, 0, 36, 60, 0, 34, 18, 0, 12, 18, 0, -72, 42, 0, -48, -108, 0, -132, 18, 0, 0, 54, 0, 0, -6, 0, -6, -144, 0, -72, 144, 0, 4, 0, 0, -138, 0, 0, -2, 72, 0, -10, -24, 0, 8, -12, 0, 54, 0, 0, 0, 18, 0, 72, -12, 0, 6, 48, 0, 0, 36, 0, 0, -18, 0, 24, -72, 0, 0, -18, 0, 44, 0, 0, -108, 0, 0, 40, -18, 0, -14, 24, 0, 6, -18, 0, -60, 18, 0, -38, -30, 0, 8, 0, 0, 0, -6, 0, 0, 36, 0, 0, -6, 0, 30, 60, 0, 64, 0, 0, 6, 0, 0, 0, 0, 0, -18, 54, 0, 0, 48, 0, 12, -6, 0, -12, -54, 0, 6, 18, 0, -44, -12, 0, 36, 12, 0, 0, -18, 0, 0, -18, 0, -12, -12, 0, 0, 0, 0, -18, 0, 0, -24, 0, 0, 22, -36, 0, 0, 72, 0, 18, 54, 0, -6, -126, 0, -20, -12, 0, 60, 0, 0, -18, -12, 0, 0, -72, 0, 0, -6, 0, 48, 36, 0, -80, 0, 0, 6, 0, 0, 216, 0, 0, -12, -126, 0, 30, -12, 0, -18, 18, 0, 6, 18, 0, 30, 18, 0, 76, -60, 0, -30, 12, 0, 0, 0, 0, 0, 0, 0, -54, 36, 0, 4, -36, 0, 72, 0, 0, 30, 0, 0, 12, -72, 0, -48, -48, 0, -40, -6, 0, 0, -36, 0, 2, -24, 0, 4, -126, 0, -108, -24, 0, 0, -72, 0, 0, 18, 0, -36, 24, 0, -72, 18, 0, 24, 0, 0, 120, 0, 0, 2, -36, 0, 14, 0, 0, 8, -54, 0, 12, 0, 0, -36, 60, 0, -88, 0, 0, -12, -36, 0, 0, 36, 0, 0, -102, 0, -60, -48, 0, -72, 54, 0, -90, 0, 0, 12, 0, 0, 68, -36, 0, 0, 36, 0, -20, 18, 0, 0, -180, 0, 4, 30, 0, -24, 18, 0, -36, -6, 0, 0, -18, 0, 0, -6, 0, -12, 96, 0, 28, -72, 0, 6, 0, 0, 0, 0, 0, -60, -36, 0, -54, 12, 0, -2, -6, 0, -18, 18, 0, 24, 6, 0, 44, 0, 0, 0, 72, 0, 0, -36, 0, 0, -24, 0, -42, 0, 0, 80, 54, 0, -12, 0, 0, -84, 0, 0, -54, -126, 0, 12, 12, 0, 18, 0, 0, -12, 54, 0, 14, -6, 0, -76, 72, 0, -42, 12, 0, 0, 0, 0, 0, -18, 0, -30, -36, 0, -64, -18, 0, -60, 0, 0, -90, 0, 0, 0, 54, 0, 0, 24, 0, 0, -72, 0, -216, -54, 0, -12, -18, 0, -12, 84, 0, 48, -72, 0, 0, 72, 0, 0, 0, 0, 108, 60, 0, 8, 0, 0, -2, 0, 0, 12, 0, 0, 12, 18, 0, 12, 0, 0, -4, 12, 0, 12, -36, 0, 62, 18, 0, -72, 30, 0, 48, 42, 0, 0, -144, 0, 0, -6, 0, 54, 48, 0, 68, 0, 0, 32, 0, 0, -18, 0, 0, -18, 0, 0, 126, 0, 0, -2, -36, 0, 162, -18, 0, -32, -36, 0, 0, 0, 0, -36, 48, 0, 0, 0, 0, 0, -12, 0, -48, -36, 0, 72, -126, 0, -68, 0, 0, 18, 0, 0, -38, 108, 0, -10, -84, 0, 16, -18, 0, 36, 0, 0, -54, -12, 0, 0, 36, 0, 54, 18, 0, 0, 0, 0, 0, 6, 0, 24, -12, 0, 88, -18, 0, 18, 0, 0, 12, 0, 0, 6, -18, 0, -56, 0, 0, -6, -48, 0, 42, -36, 0, 2, 36, 0, -72, 0, 0, 48, -12, 0, 0, 126, 0, 0, -18, 0, -36, 36, 0, 0, -72, 0, 52, 0, 0, 0, 0, 0, -6, 0, 0, -48, -72, 0, 2, -18, 0, 0, 0, 0, -42, 54, 0, -16, 36, 0, 108, -108, 0, 0, -54, 0, 0, -6, 0, -114, -96, 0, 0, 126, 0, 6, 0, 0, -108, 0, 0, 54, -36, 0, 12, -60, 0, -12, 24, 0, -12, -18, 0, 48, -6, 0, -64, 0, 0, -12, 54, 0, 0, -36, 0, 0, 6, 0, 126, -48, 0, 8, -108, 0, -8, 0, 0, -12, 0, 0, -10, 126, 0, 0, 36, 0, -4, -6, 0, 36, 108, 0, -12, 36, 0, 64, 0, 0, 114, -12, 0, 0, 36, 0, 0, -18, 0, -18, -60, 0, 56, -36, 0, 48, 0, 0, 24, 0, 0, 20, 144, 0, 48, 36, 0, 54, 132, 0, -66, 36, 0, 6, 12, 0, -36, -84, 0, 30, 66, 0, 0, 72, 0, 0, 108, 0, 12, -12, 0, -96, 36, 0, 2, 0, 0, 6, 0, 0, 112, -36, 0, 0, 96, 0, -60, 0, 0, 0, 0, 0, -8, 12, 0, -72, 216, 0, -24, 6, 0, 0, 126, 0, 0, -42, 0, 108, 180, 0, -36, 0, 0, 72, 0, 0, -72, 0, 0, 26, -108, 0, -20, -12, 0, 12, -18, 0, 0, 18, 0, 0, 12, 0, -72, -18, 0, -18, -36, 0, 0, -36, 0, 0, 36, 0, -24, 36, 0, 4, 126, 0, -18, 0, 0, 90, 0, 0, -32, 36, 0, -18, -108, 0, 18, 18, 0, 0, 144, 0, -14, -66, 0, -72, 0, 0, 36, -36, 0, 0, -18, 0, 0, -12, 0, 6, 12, 0, 72, -36, 0, -30, 0, 0, 0, 0, 0, 8, 72, 0, -64, 0, 0, -54, 12, 0, 54, 0, 0, -6, -90, 0, -176, 0, 0, 36, 78, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, -108, 216, 0, 134, 0, 0, 42, 0, 0, 0, 54, 0, -2, -216, 0, -28, -12, 0, 12, 108, 0, 64, 6, 0, -72, 84, 0, 18, 0, 0, 0, -72, 0, 0, 18, 0, 6, -60, 0, 144, -126, 0, 4, 0, 0, -126, 0, 0, 24, 0, 0, 36, 60, 0, -4, -84, 0, 6, -18, 0, -6, -36, 0, 148, 0, 0, -12, -30, 0, 0, -36, 0, 0, -78, 0, 90, -96, 0, 76, 54, 0, -10, 0, 0, 60, 0, 0, 30, 54, 0, -54, -48, 0, -108, 24, 0, -162, 0, 0, -80, -96, 0, 48, -54, 0, 12, 6, 0, 0, 108, 0, 0, -12, 0, 0, 108, 0, 48, -54, 0, -24, 0, 0, 36, 0, 0, 0, -72, 0, 40, 0, 0, 2, 48, 0, 36, -54, 0, -12, -24, 0, 288, -12, 0, 12, -108, 0, 0, 54, 0, 0, -36, 0, -216, 12, 0, 72, -36, 0, 18, 0, 0, -12, 0, 0, -102, 54, 0, 84, 24, 0, 78, 12, 0, -24, 180, 0, 18, 12, 0, 96, 0, 0, -48, 12, 0, 0, -36, 0, 0, 48, 0, 54, 36, 0, -8, 36, 0, 0, 0, 0, -96, 0, 0, 48, -126, 0, 48, 144, 0, 0, 18, 0, 60, 0, 0, 42, -18, 0, 72, -12, 0, 12, -6, 0, 0, -54, 0, 0, 30, 0, 144, 84, 0, -12, 36, 0, -24, 0, 0, -54, 0, 0, -72, -36, 0, 18, 36, 0, 0, 0, 0, 36, -72, 0, 56, 6, 0, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 24, 0, -84, -24, 0, 20, 18, 0, -12, 0, 0, -6, 0, 0, -4, 126, 0, -30, 48, 0, 6, 0, 0, 36, 54, 0, 0, 18, 0, -4, 30, 0, -24, 48, 0, 0, 108, 0, 0, -12, 0, -174, 72, 0, 16, -162, 0, 116, 0, 0, -48, 0, 0, -76, 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, 5, 1, 6, 0]], "char_orbit_index": 45, "prim_orbit_index": 5, "minimal_twist": "130.2.l.a", "char_is_minimal": true, "conrey_index": 361, "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], [1, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, -1, 0], [0, -3, 0, 3], [0, 0, 0, 0], [3, 0, 1, 0], [3, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [3, 3, -3, -6], [0, 0, 0, 0], [-2, 3, -2, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-3, 0, 3, 0], [0, 2, 6, 2], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 4, 0, -3], [0, 0, 0, 0], [0, 3, 0, -3], [0, 2, -6, 2], [0, 0, 0, 0], [1, 0, -2, -3], [0, -1, 0, 0], [0, 0, 0, 0], [3, 0, -6, -3], [3, 0, -3, 0], [0, 0, 0, 0], [6, -6, -3, 6], [3, -4, 0, 2], [0, 0, 0, 0], [-1, 0, 0, 0], [12, 0, -6, 0], [0, 0, 0, 0], [-2, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 0], [2, 6, 2, 0], [0, 0, 0, 3], [0, 0, 0, 0], [0, 0, 2, 0], [0, -1, 0, 1], [0, 0, 0, 0], [4, 0, -3, 0], [3, -4, 0, 2], [0, 0, 0, 0], [0, 0, 3, 0], [3, 0, -3, 0], [0, 0, 0, 0], [2, -6, 2, 0], [-6, 0, -6, 0], [0, 0, 0, 0], [-1, -3, 1, 6], [0, -1, -3, -1], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, -3, -3], [0, 0, 0, 0], [0, 0, 0, -3], [0, 6, 0, 0], [0, 0, 0, 0], [5, 0, -10, -3], [-6, 3, 6, -6], [0, 0, 0, 0], [-4, 3, 2, -3], [-9, 0, 0, 0], [0, 0, 0, 0], [1, -6, 0, 3], [0, -1, 0, 1], [0, 0, 0, 0], [0, 6, 0, -12], [3, 0, -6, -3], [0, 0, 0, 0], [-3, -3, -3, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 3, 0], [6, -12, -3, 12], [0, 0, 0, 0], [0, 9, 0, 3], [6, 4, 0, -2], [0, 0, 0, 0], [0, 0, 3, 0], [3, -2, -3, 4], [0, 0, 0, 0], [7, -3, 7, 0], [0, 2, 0, 0], [0, 0, 0, 0], [-1, 0, 1, 0]]}