# Stored data for newform 1110.2.bb.b, downloaded from the LMFDB on 23 April 2024.
{"label": "1110.2.bb.b", "space_label": "1110.2.bb", "level": 1110, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505455086797910, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1350755218130250124, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [1, 0, -1, 0, 1]], [11, [0, 1]]], "qexp_display": "q+(\\zeta_{12}-\\zeta_{12}^{3})q^{2}+\\zeta_{12}q^{3}+(1-\\zeta_{12}^{2}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 185, "char_orbit_label": "bb", "char_is_real": false, "Nk2": 4440, "analytic_conductor": 8.863394624362122, "hecke_ring_index": 1, "level_radical": 1110, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [1110, 6, [371, 667, 631], [6, 3, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 3, 5, 37], "conrey_indexes": [1009, 1099], "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": "0.067", "prec": 17}, {"__RealLiteral__": 0, "data": "3.993", "prec": 17}, {"__RealLiteral__": 0, "data": "2.485", "prec": 17}, {"__RealLiteral__": 0, "data": "99.764", "prec": 20}, {"__RealLiteral__": 0, "data": "140.618", "prec": 24}, {"__RealLiteral__": 0, "data": "3996.074", "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, -2, 0], "traces": [0, 4, 0, 0, 2, -2, 4, 0, 0, 2, -8, 0, 0, 0, 4, -4, -2, 0, 0, 14, 2, 2, 0, 0, 2, 6, 20, 0, 0, 12, -2, 8, 0, 0, 4, -4, 4, 0, 0, 10, -4, 0, 0, 0, 0, -4, 8, 0, 0, -12, 8, 8, 0, 0, 2, 0, 2, 0, 0, 0, -8, 8, 0, 0, -4, -20, 0, 0, 0, -8, -2, 26, 0, 0, 22, 16, -14, 0, 0, -20, 4, -2, 0, 0, 4, -16, -4, 0, 0, -24, -4, 10, 0, 0, 8, 14, -2, 0, 0, 0, 12, 8, 0, 0, 10, -4, -16, 0, 0, -12, 0, 20, 0, 0, 14, 16, 6, 0, 0, 8, 2, -44, 0, 0, 4, -44, 2, 0, 0, 4, -10, 24, 0, 0, -16, 4, -4, 0, 0, -24, -8, -8, 0, 0, 2, -6, 16, 0, 0, -20, 6, 24, 0, 0, 0, -4, 20, 0, 0, -32, 4, -8, 0, 0, 0, 0, -18, 0, 0, 24, 4, 28, 0, 0, 12, 16, 0, 0, 0, -48, -2, -24, 0, 0, 16, -40, 8, 0, 0, -2, -28, -16, 0, 0, 16, -20, -24, 0, 0, 40, -8, -8, 0, 0, 4, 0, 10, 0, 0, 0, -4, 28, 0, 0, 16, -8, 4, 0, 0, -16, 0, 40, 0, 0, -2, -6, -26, 0, 0, -20, -16, 0, 0, 0, 10, 16, 0, 0, 0, 14, -4, -28, 0, 0, -8, 24, 0, 0, 0, -36, -4, -48, 0, 0, 18, -4, -2, 0, 0, 20, -40, 6, 0, 0, 0, 64, 14, 0, 0, -12, -4, -36, 0, 0, 14, 0, 8, 0, 0, 4, 2, 32, 0, 0, -26, -56, 0, 0, 0, -26, -24, -16, 0, 0, -12, 0, 2, 0, 0, -40, 8, 4, 0, 0, -28, 8, 8, 0, 0, -10, -16, -40, 0, 0, 6, 4, 20, 0, 0, 0, 2, 8, 0, 0, 2, 80, -40, 0, 0, -8, 0, -38, 0, 0, -48, 16, 2, 0, 0, -52, -8, 0, 0, 0, -8, -8, -8, 0, 0, 20, 6, -10, 0, 0, 0, 26, -48, 0, 0, -140, -8, -60, 0, 0, 20, 32, 8, 0, 0, 0, -2, -32, 0, 0, 0, 4, 16, 0, 0, -26, 28, 36, 0, 0, -4, 0, -20, 0, 0, -38, -20, 16, 0, 0, 52, -20, 0, 0, 0, 28, 6, 24, 0, 0, 4, -2, 12, 0, 0, 70, 0, -14, 0, 0, -8, 72, -10, 0, 0, 80, -2, 88, 0, 0, 16, 16, 26, 0, 0, 0, 8, 70, 0, 0, 8, -12, -24, 0, 0, 44, 0, 12, 0, 0, 22, 48, -16, 0, 0, -16, 16, 0, 0, 0, -12, -20, -14, 0, 0, 4, -16, 78, 0, 0, -6, -8, -54, 0, 0, -8, -16, 12, 0, 0, -20, 84, 4, 0, 0, 48, 4, 100, 0, 0, -22, 32, -2, 0, 0, -80, 24, 152, 0, 0, 70, 0, -4, 0, 0, 18, -22, -24, 0, 0, 4, -4, 0, 0, 0, -62, -16, -16, 0, 0, 10, 20, -4, 0, 0, -16, 10, 20, 0, 0, 48, -6, -120, 0, 0, 28, -16, 0, 0, 0, -24, -16, -8, 0, 0, 0, -4, -152, 0, 0, -8, 24, 10, 0, 0, 16, 0, 42, 0, 0, 100, -22, -48, 0, 0, 20, -4, 0, 0, 0, 8, 104, 96, 0, 0, -24, 14, -82, 0, 0, 0, 32, -2, 0, 0, 20, 6, -36, 0, 0, 32, 20, 24, 0, 0, 28, 0, 104, 0, 0, 0, -4, -10, 0, 0, 66, 12, -36, 0, 0, -24, 22, 8, 0, 0, 6, -16, -40, 0, 0, -8, 0, 0, 0, 0, 80, 4, -16, 0, 0, 10, 14, -56, 0, 0, 44, -4, -96, 0, 0, 16, -72, -16, 0, 0, 52, 8, -28, 0, 0, 8, 4, -28, 0, 0, 0, 30, 4, 0, 0, -12, -48, 0, 0, 0, -40, 0, -28, 0, 0, 18, -56, 20, 0, 0, 16, 8, 0, 0, 0, 8, 8, 48, 0, 0, -16, 8, -6, 0, 0, 14, 28, -26, 0, 0, -160, 16, 10, 0, 0, 10, 48, 6, 0, 0, 54, 8, 20, 0, 0, 0, -8, -62, 0, 0, -16, -52, -40, 0, 0, 8, 0, -24, 0, 0, -50, 2, -10, 0, 0, 24, 18, -44, 0, 0, -4, -32, -8, 0, 0, -20, -24, 8, 0, 0, 28, -44, 140, 0, 0, 4, 10, 76, 0, 0, 8, -44, -136, 0, 0, 60, 24, 2, 0, 0, 0, 28, 60, 0, 0, -8, -8, -88, 0, 0, -28, 0, 20, 0, 0, 4, 12, 32, 0, 0, 0, -10, 0, 0, 0, -12, -24, 24, 0, 0, -60, 40, -52, 0, 0, -4, 16, 20, 0, 0, 16, -16, 24, 0, 0, -16, -8, 40, 0, 0, 36, 4, 40, 0, 0, 0, 160, -4, 0, 0, -10, 0, -42, 0, 0, 20, 0, 0, 0, 0, 92, -18, 50, 0, 0, -24, 48, 0, 0, 0, 96, -8, -80, 0, 0, 14, -48, -8, 0, 0, 48, 24, -8, 0, 0, 8, -14, 8, 0, 0, -164, 8, 0, 0, 0, 2, 32, 52, 0, 0, 0, -6, -40, 0, 0, 112, 4, 16, 0, 0, 12, 0, -24, 0, 0, 20, 0, -78, 0, 0, 36, 48, 0, 0, 0, -20, 24, -4, 0, 0, 24, 6, -32, 0, 0, 26, -24, 24, 0, 0, 4, -20, -4, 0, 0, -104, -32, 20, 0, 0, 32, -8, 8, 0, 0, 0, 88, 44, 0, 0, -8, -4, -168, 0, 0, -54, 0, 20, 0, 0, -112, -16, -10, 0, 0, 0, -2, 0, 0, 0, -80, -56, 32, 0, 0, -32, 8, 28, 0, 0, -14, 4, -108, 0, 0, 28, -40, -8, 0, 0, 28, -32, -20, 0, 0, 18, -30, -16, 0, 0, 0, 12, 12, 0, 0, 0, -208, 12, 0, 0, 32, 0, 32, 0, 0, 26, -20, -18, 0, 0, -2, -8, 0, 0, 0, -24, 16, -12, 0, 0, -20, -16, 4, 0, 0, 24, -12, -18, 0, 0, 68, 4, 88, 0, 0, 2, 0, 28, 0, 0, 26, -20, -8, 0, 0, 0, 32, 22, 0, 0, -80, -20, -10, 0, 0, 12, 0, -48, 0, 0, 68, 16, -66, 0, 0, 8, -14, 0, 0, 0, -124, 32, 52, 0, 0, -14, -104, 0, 0, 0, -80, -8, 4, 0, 0, -48, -16, -6, 0, 0, -180, -2, -64, 0, 0, -72, -8, -24, 0, 0, -22, 24, 64, 0, 0, -24, -16, 28, 0, 0, 12, 0, -10, 0, 0, 16, -20, -20, 0, 0, -136, -40, 0, 0, 0, 24, -32, 8, 0, 0, 38, 4, 0, 0, 0, 64, -22, 42, 0, 0, 54, -26, 30, 0, 0, -2, 12, -52, 0, 0, -32, -28, -80, 0, 0, 0, -20, -16, 0, 0, -44, -24, 48, 0, 0, -64, 0, 26, 0, 0, -56, -12, 8, 0, 0, 16, -108, 0, 0, 0, -24, -20, 22, 0, 0, 124, 32, -24, 0, 0, -24, 0, -36, 0, 0, -20, 80, -52, 0, 0, 0, -16, 4, 0, 0, 40, -28, 40, 0, 0, 0, -8, 46, 0, 0, -4, -28, -8, 0, 0, 20, 88, -16, 0, 0, -50, 8, -14, 0, 0, -64, 16, 0, 0, 0, 4, 36, 62, 0, 0, 200, 0, -112, 0, 0, 62, -280, 10, 0, 0, 0, -8, 32, 0, 0, -80, 18, -24, 0, 0, -132, 96, 24, 0, 0, 0, 24, -6, 0, 0, 120, -4, -80, 0, 0, 40, 0, 28, 0, 0, -16, 18, 0, 0, 0, -60, 12, 0, 0, 0, 64, -2, 16, 0, 0, 16, -40, -8, 0, 0, 176, -8, 26, 0, 0, 168, -22, 4, 0, 0, -52, 40, -52, 0, 0, 40, -12, 200, 0, 0, 0, -48, 56, 0, 0, -16, 120, 8, 0, 0, 42, 0, 220, 0, 0, -76, -64, 40, 0, 0, 78, 14, 0, 0, 0, 24, -48, -24, 0, 0, -50, 32, -10, 0, 0, -2, 6, -176, 0, 0, -182, -6, 20, 0, 0, -36, 72, -26, 0, 0, 48, 8, 264, 0, 0, 0, 20, 24, 0, 0, 146, -28, -52, 0, 0, -20, 0, -4, 0, 0, 104, -16, 36, 0, 0, 8, -100, 0, 0, 0, 22, 48, 40, 0, 0, 0, -8, 40, 0, 0, -4, 12, 54, 0, 0, 10, -64, 14, 0, 0, 52, 16, -36, 0, 0, 8, -96, 0, 0, 0, 0, 52, -36, 0, 0, -24, 56, 16, 0, 0, -112, 0, -16, 0, 0, 14, 0, -70, 0, 0, 10, -4, 0, 0, 0, -120, -26, -28, 0, 0, -16, 24, 280, 0, 0, 52, -16, 10, 0, 0, 46, -32, -18, 0, 0, -8, -24, 200, 0, 0, -260, 24, -116, 0, 0, 0, 0, 0, 0, 0, 24, 20, -64, 0, 0, -16, 0, 104, 0, 0, 6, 40, 52, 0, 0, -36, -40, 0, 0, 0, 24, -4, 140, 0, 0, 8, 4, -48, 0, 0, -24, -48, 156, 0, 0, -106, -8, -52, 0, 0, -24, 14, -24, 0, 0, 18, 48, -12, 0, 0, 0, -4, -52, 0, 0, 0, -16, -2, 0, 0, 14, 0, 32, 0, 0, -40, -10, 72, 0, 0, -40, 16, 0, 0, 0, 20, 80, 38, 0, 0, -2, -40, 16, 0, 0, 32, 224, 6, 0, 0, -24, 6, -76, 0, 0, 36, 8, -52, 0, 0, 154, -40, 16, 0, 0, 0, -64, 40, 0, 0, -6, 64, 4, 0, 0, -72, 0, 14, 0, 0, 0, -6, -48, 0, 0, 12, -16, 0, 0, 0, 100, 16, -24, 0, 0, -12, -56, -4, 0, 0, -72, -4, 4, 0, 0, 6, 20, -36, 0, 0, -48, -40, 54, 0, 0, -56, -24, 140, 0, 0, 0, 0, 24, 0, 0, 14, -8, -82, 0, 0, 32, 0, 180, 0, 0, -20, 76, 8, 0, 0, -40, 36, 0, 0, 0, -20, 4, -48, 0, 0, -20, 24, 48, 0, 0, 4, -64, 160, 0, 0, -128, 2, 82, 0, 0, 44, -8, 32, 0, 0, -42, -48, -336, 0, 0, -44, 26, 32, 0, 0, 50, -16, -4, 0, 0, -26, 0, 68, 0, 0, 62, -56, 0, 0, 0, -14, -52, 0, 0, 0, -8, 4, 120, 0, 0, -70, -48, -68, 0, 0, 140, -8, -128, 0, 0, -26, 20, 4, 0, 0, -8, -24, 8, 0, 0, -12, -40, -16, 0, 0, 0, -44, 20, 0, 0, -58, -10, -44, 0, 0, -80, 0, 62, 0, 0, -12, 248, -48, 0, 0, 24, 0, 0, 0, 0, -48, 156, 2, 0, 0, 52, 24, -70, 0, 0, -32, -8, 112, 0, 0, -132, 96, 20, 0, 0, -40, 70, 16, 0, 0, 20, 8, -58, 0, 0, 0, 120, 4, 0, 0, 8, 48, -60, 0, 0, -208, 44, -6, 0, 0, 32, -10, -100, 0, 0, -28, 64, 0, 0, 0, 0, 8, -116, 0, 0, 24, 20, 8, 0, 0, 124, -32, -60, 0, 0, 156, 0, 130, 0, 0, 156, 60, 124, 0, 0, -10, 16, -12, 0, 0, 0, -16, 320, 0, 0, -108, -76, -40, 0, 0, 24, 0, 48, 0, 0, -48, 48, -16, 0, 0, 112, -8, 0, 0, 0, 6, -60, 0, 0, 0, -12, 4, 16, 0, 0, -14, 52, 20, 0, 0, 14, 42, 76, 0, 0, -4, -18, 2, 0, 0, -72, 32, 60, 0, 0, 0, 88, 96, 0, 0, 28, 2, -52, 0, 0, 110, 0, 8, 0, 0, 8, 40, -76, 0, 0, 188, -16, 22, 0, 0, 50, -32, 84, 0, 0, 2, -38, -24, 0, 0, 98, 80, -80, 0, 0, -102, -32, -40, 0, 0, 100, 48, -176, 0, 0, 76, 48, 44, 0, 0, 0, 52, -32, 0, 0, -8, -120, -70, 0, 0, 96, 0, 48, 0, 0, -8, -8, -38, 0, 0, 20, -80, 0, 0, 0, -106, -14, -18, 0, 0, -80, 22], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 185, 14, 1, 6, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 37, 3, 1, 3, 0]], "char_orbit_index": 28, "prim_orbit_index": 14, "minimal_twist": "1110.2.bb.b", "char_is_minimal": true, "conrey_index": 1009, "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, 1, 0, 0], [1, 0, -1, 0], [-1, -2, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, -1], [0, 0, 1, 0], [-2, 0, 0, 1], [0, 0, 0, 0], [0, 1, 0, -1], [0, 5, 0, 0], [1, 0, 0, 0], [0, -1, -2, 1], [0, 0, -1, 0], [0, 2, 0, -2], [0, 1, 0, 0], [7, 0, -7, 0], [0, -2, 1, 2], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 4], [1, 0, -1, 0], [0, 4, 3, -4], [5, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, -1], [3, 0, 0, 0], [-1, -2, 1, 0], [2, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [2, 0, -2, 0], [0, -1, -2, 1], [1, 0, 0, 0], [0, 7, 0, -3], [0, 0, 0, -7], [0, 0, 5, 0], [-2, 1, 2, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-1, 0, 0, -2], [0, 0, 4, 0], [0, 0, 0, 4], [0, 0, 0, -1], [0, 0, -6, 0], [4, 3, -4, 0], [2, 0, 0, 0], [0, 5, 0, -5], [0, -8, 0, 8], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 7, 0, -7], [0, 3, 0, -3], [0, 0, 0, 0], [-2, 0, 0, 1], [4, 0, -4, 0], [0, 2, 0, -2], [0, 0, 0, 1], [-1, 0, 0, 0], [0, -5, -10, 5], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, -2], [-4, 0, 4, 0], [-1, -2, 1, 0], [13, 0, -13, 0], [0, 1, 0, -1], [0, 0, 0, 8], [7, 0, -3, 0], [4, 0, 0, 3], [0, 0, -7, 0], [0, 0, 0, 0], [0, 5, 0, 0], [-10, 0, 10, 0], [1, 0, 0, 2], [-1, 0, 1, 0], [0, 0, 0, 0], [0, -9, 0, 9], [1, 0, 0, 0], [-4, 0, 0, 2], [0, 0, -2, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, -12, 0], [0, -1, -2, 1], [0, 0, 5, 0], [0, 4, 0, 0], [0, 2, 0, 0], [0, 0, 4, 0], [0, -14, 7, 14], [0, 0, -1, 0], [0, 0, 0, 8], [0, -6, 0, 0], [0, 0, 0, 0], [3, 0, 0, -4]]}