# Stored data for newform 1110.2.x.a, downloaded from the LMFDB on 25 April 2024.
{"label": "1110.2.x.a", "space_label": "1110.2.x", "level": 1110, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1580581520470, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 403639118979844467, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [121, 22, 15, -2, 1]]], "qexp_display": "q-\\zeta_{12}q^{2}+\\zeta_{12}^{2}q^{3}+\\zeta_{12}^{2}q^{4}+(-\\zeta_{12}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 37, "char_orbit_label": "x", "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": "0.193", "prec": 17}, "analytic_rank_proved": true, "char_values": [1110, 6, [371, 667, 631], [6, 6, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 37], "conrey_indexes": [751, 841], "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": "0.064", "prec": 17}, {"__RealLiteral__": 0, "data": "3.906", "prec": 17}, {"__RealLiteral__": 0, "data": "0.784", "prec": 17}, {"__RealLiteral__": 0, "data": "58.405", "prec": 20}, {"__RealLiteral__": 0, "data": "9.283", "prec": 17}, {"__RealLiteral__": 0, "data": "1384.951", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 2, 0, 2], "traces": [0, 4, 0, 2, 2, 0, 0, 2, 0, -2, 4, 8, -2, 0, 0, 0, -2, -12, 0, 0, 0, -2, 0, 0, 0, 2, -4, -4, -2, 0, 2, 0, 0, 4, 4, 12, -4, 0, -12, 0, 2, -2, -12, 0, 4, 0, 6, 12, -4, -12, 0, 0, 0, 2, 0, 0, -12, 0, 4, -18, 0, 6, 4, -4, -4, -2, 0, 0, 0, 6, 2, 12, 0, 44, -2, 4, 0, 4, -2, 18, 0, -2, 0, 6, -4, 8, -6, 6, 0, 12, -2, -12, 6, 12, 6, -6, 0, 0, -24, -4, 4, -8, -4, 0, -2, 0, -6, 0, -2, 0, 8, 0, -4, 12, -6, -6, 6, 0, 2, 0, -2, -28, -44, 2, 12, 0, -12, 14, 0, 18, 0, -30, -4, -36, 0, 0, -4, 0, 12, 0, 0, 6, 0, 0, -2, -4, -18, -24, 0, 36, 0, -32, -6, 12, 0, -4, 0, -12, -20, 4, -2, 42, 0, -54, 2, 0, 24, -36, -12, -24, -12, 0, 18, 24, 8, 4, -4, 0, -12, 0, 0, 32, -2, 6, 12, 20, 8, -24, 6, -2, 0, 0, -2, 0, 6, -4, -24, -2, 0, 0, 0, 0, 12, 30, 12, 18, 8, 6, 0, 0, -2, 32, 4, -12, 0, 6, 0, 36, 4, 22, 0, -8, -22, -64, -12, 2, 18, -6, 0, 28, 0, -4, 8, 24, 2, 6, 0, 18, 20, 60, 0, -12, 0, 2, 6, 0, -18, 6, 8, 12, 2, 0, -2, 0, -12, 4, -2, 24, -12, -48, -4, 6, 10, -26, 0, 0, -6, 0, 0, 52, -4, -16, 12, 0, 6, 4, 6, 36, 48, 12, -2, -6, 0, 0, -12, -12, -8, -34, 0, -2, 0, 42, 22, -6, -24, 4, -22, -8, 24, 6, 2, -18, 0, -4, 0, -22, -8, 44, -4, 18, 0, -36, 2, -36, -6, -12, 18, -6, -6, 0, 0, 0, 36, -24, 2, 0, 14, 0, -18, 18, 4, -48, 12, 0, -48, 12, -2, -20, 0, 0, 4, 0, 6, -92, -12, 6, 24, 0, 6, -48, 12, 0, 0, -96, -2, -18, 0, -12, -12, -8, -4, -20, 0, -14, 0, -18, -22, 18, 6, 4, 0, -20, 12, 24, 8, 0, 0, 4, 0, -44, -12, 28, 24, -24, 0, 24, 38, 18, 42, 90, 0, 0, -24, 0, 30, -10, -8, 64, -10, 0, 2, 0, -12, 4, -4, 0, 32, 0, -8, 30, -2, 0, 18, 0, 6, 0, 2, 0, -24, 34, -12, 0, 30, -6, -6, -12, 18, -126, 0, 0, 0, -48, 2, -36, 56, 4, 0, 18, 0, 18, 4, -12, 12, 4, 0, -24, 12, 18, -2, 0, 0, -4, 0, 32, 56, -4, 6, 60, 0, 12, 6, 78, -24, -42, 6, 4, 42, 0, 0, -24, 12, -24, -2, 0, -10, 0, -12, 2, 2, -60, -4, -20, -32, 42, -14, -6, 0, 0, -22, 0, -12, -40, 4, -4, 0, 0, 12, 24, 24, -120, 0, -36, 4, 126, 0, 12, 12, -48, 28, -22, 0, -14, 0, 0, 6, -8, 18, 24, -22, 48, 0, 10, 4, -6, 0, 2, 0, -16, -8, 44, 2, 18, 0, -18, 12, 36, -12, -12, 12, -24, 0, 0, -72, -32, -8, 8, 2, 0, 0, 0, 0, 12, 6, -42, -4, -2, 0, 0, 4, -6, -12, 0, -10, 0, -6, 36, 8, 2, 18, 0, 0, 32, 0, 36, -6, -6, 2, -30, 0, -6, 4, 108, 12, 4, 0, -2, 0, -78, -12, 12, -18, -4, 0, -80, 0, -20, 18, -42, 0, 16, 0, 0, 60, 0, 32, 0, 0, -42, 6, 30, 6, -6, 12, -4, -66, 0, -24, 44, 16, -128, 4, 0, -8, 0, 0, -2, 4, 0, -24, -4, -4, 6, -10, 16, -30, 0, 2, 0, 8, -24, -4, 14, -36, 0, 42, -6, 36, -36, 0, -36, -2, 36, 0, -18, -4, 20, 4, -22, 0, -6, 0, -114, -14, -4, 24, -12, -20, -36, -36, -32, 0, 12, 0, 34, 0, -2, -48, 76, -18, 78, 0, -6, 8, -12, 0, 6, -12, -28, 18, 0, 6, -16, 48, -8, -16, 0, 4, 0, -24, 12, 2, 72, 4, -60, -8, 6, -10, 20, 18, 0, 12, 0, 12, -48, 40, -4, -12, 0, -30, 36, 0, 66, 0, -12, -32, -6, 0, 66, 2, 4, 44, -48, 0, 92, 0, -24, 6, 0, -18, -8, -2, 12, 6, 32, 4, 24, 0, 6, 0, -72, 4, 60, -6, 48, 0, -12, 2, 84, 42, 12, 0, 42, -12, 0, 36, -4, -40, -4, 2, 0, 4, 0, -6, 68, -6, -12, 12, -84, -16, -54, -2, 24, -24, 0, -12, 0, -10, -20, -4, 26, 18, 0, 0, 22, 60, -6, -42, -126, 6, -24, 0, -12, 0, 88, 0, 18, 0, 26, 0, 0, -2, 20, 30, -32, -4, 28, 12, -18, 28, 12, 0, -78, 0, 26, 16, 8, 34, -6, 0, -72, 6, 36, 0, 24, 48, -24, 0, 0, 30, 12, -4, 88, -60, 0, 16, 0, -6, -14, 2, 0, 8, 66, -24, 192, -10, -6, -36, 0, -4, 0, -6, -68, 36, -12, 0, 0, -78, 2, 36, 36, 6, -12, -4, 42, 0, 12, -22, 112, 100, 6, 0, -12, 0, -54, -4, 2, 48, -120, -20, -20, 12, -4, -32, -18, 0, 12, 0, -6, -128, -40, -2, -24, 0, -18, -18, -36, 12, 180, -6, 4, -12, 0, 0, 12, -32, -44, -28, 0, -4, 0, 6, 22, -32, 18, -8, 0, -40, 18, 4, -56, 12, 0, 12, 0, -16, 16, 4, -52, -12, 0, 6, -6, -6, 48, 18, -12, -12, 30, 0, 18, -6, -12, 40, -44, 0, -24, 0, 12, 24, 12, 0, 60, 0, 0, -12, -38, 18, 102, 0, -12, 0, -76, 4, 192, 16, 0, 0, -48, -14, 24, -24, 0, -72, 18, -18, 0, -12, -18, 12, 0, -4, 0, 4, 0, -54, 10, 6, -72, -4, 0, 4, -24, -24, 40, 48, 0, -10, 0, 2, 44, -8, 20, 12, 0, 0, 16, -12, -12, -84, -72, -4, -18, 0, 24, 2, -4, 12, 10, 0, -46, 0, -48, -6, 52, 12, 12, -84, -112, 24, -106, -2, -30, 0, 66, 0, -12, 44, -96, -10, 192, 0, -24, 26, 0, 0, 30, 0, 56, -36, 0, -6, 20, -4, -76, 6, 0, 2, 0, -12, 0, 0, -12, 0, 44, -24, -18, 26, -4, -48, 0, -2, 0, -50, -40, -32, 28, 36, 0, 12, 14, 0, 24, 12, -72, -32, -18, 0, -12, 22, -48, 8, -18, 0, 72, 0, 12, 26, 2, 36, -104, 0, -16, 48, -10, -28, 12, 0, 24, 0, -24, -4, -12, -8, 54, 0, 0, 24, 108, -6, 54, 12, -4, 0, 0, 12, 28, -24, -88, -42, 0, -6, 0, -66, 14, -4, -12, 48, 44, -68, -24, -6, -16, 0, 0, 2, 0, 2, 24, 76, 66, 6, 0, 60, 86, 42, 42, -12, 90, -22, -180, 0, -36, 6, 0, -96, 6, 0, 0, 0, 30, 2, 44, 30, -48, -20, -20, 72, -6, -4, 30, 0, 32, 0, 28, -20, 4, -6, 36, 0, 0, -2, -18, -24, -36, -18, -16, -12, 0, 12, -4, -28, 144, 4, 0, -60, 0, 0, 24, 16, 12, -44, 0, -12, 24, -4, 12, 42, 0, 22, 0, 2, -40, -8, 0, 30, 0, 18, -52, 0, 6, 12, -168, -6, 24, 0, 24, -12, -12, 4, 8, 0, 0, 0, -84, -12, -4, -6, 68, 48, -148, -12, 6, 10, -12, 0, -12, 0, 40, -12, -12, 14, 24, 0, -36, 12, -12, 12, -54, 18, -94, 0, 0, -18, 76, 0, 12, 46, 0, 18, 0, 18, 8, -12, -48, -96, -2, 4, -6, 4, -18, 0, 0, 28, 0, -14, 8, -140, 30, 0, 0, -30, -18, -18, -12, 18, -6, -18, 18, 0, 180, -4, -52, -4, 12, 0, -2, 0, 132, 6, 2, -36, -144, 0, -48, -30, -12, -24, 180, 0, 8, 0, -18, -88, -112, 2, 12, 0, 0, 20, 54, 0, 222, 0, 4, -78, 0, -12, -12, 180, 64, -4, 0, 28, 0, 24, -2, 44, 24, 12, -94, 0, 60, -46, -2, 12, 0, -6, 0, -2, 116, 12, -6, -6, 0, 24, -2, -24, 54, -30, -42, 0, -36, 0, -102, 40, 8, -96, 28, 0, -22, 0, -30, 60, 60, 0, -20, 0, -48, 0, -106, 6, 12, 0, -12, 0, 4, -4, -8, -60, 36, 0, 84, 10, 54, -12, 0, -48, 24, -12, 0, 0, -2, -24, 0, -2, 0, -4, 0, -18, 52, -2, -60, 88, 2, -40, -48, -16, 62, 36, 0, -4, 0, 14, -8, -8, 6, 12, 0, 0, 112, -18, 66, 72, -72, 22, -102, 0, 54, -18, -36, -24, -96, 0, -20, 0, -18, 2, 76, 18, -8, 0, -8, 0, 42, -10, 0, 0, -88, 0, -46, 36, 48, -24, -6, 0, 6, -8, -120, -36, -24, 0, 30, 66, 0, -6, 30, 8, 0, -4, 0, -32, 0, 12, -48, 2, 12, -88, -72, 24, 120, -6, -24, -42, 0, 14, 0, -4, -44, 48, 0, 12, 0, -24, 14, 18, -66, 0, 6, 40, 0, 0, 36, -6, 64, 76, 8, 0, 20, 0, 18, -4, 12, 42, 96, -20, -16, 90, 24, 6, 204, 0, -8, 0, -10, 0, 8, -4, 84, 0, -6, -12, -18, 30, 0, -102, -2, 30, 0, 6, -44, -20, -32, -42, 0, -4, 0, -6, 22, 32, 162, 4, -66, -20, 18, -2, -8, 36, 0, 0, 0, -2, -24, 24, -4, -36, 0, -36, 56, -12, -60, 42, -12, -4, -102, 0, 36, 4, -48, -192, 54, 0, 38, 0, -30, 16, 2, -72, -260, 0, -64, -54, 96, -4, -18, 0, 4, 0, -64, 4, 72, 2, 24, 0, 0, 0, 42, 108, -6, 18, -72, 0, 0, 6, -12, -120, -28, -6, 0, 40, 0, 24, -64, -2, 144, 4, -22, 48, 174, 0, 64, -36, 0, -12, 0, -4, 0, 68, 6, 12, 0, -12, 26, -24, 24, -12, -24, 10, -108, 0, 30, -24, 72, -12, -128, 0, 18, 0, -228, 4, -100, -12, 4, 42, -20, 18, -8, 0, 78, 0, 2, 0, -14, 0, 64, 54, -12, 0, 48, 6, 36, 18, -84, -6, -14, -48, 0, 108, -24, 4, 12, 24, 0, -18, 0, 48, 16, 28, -6, -40, 18, 8, 216, 0, 54, 0, 0, 6, 0, -18, 8, 4, -20, 18, 0, 54, 2, 18, 72, 102, 150, -4, -78, 0, -72, 12, -20, -36, -12, 0, 38, 0, 84, 2, -2, 36, 24, 0, 112, 72, -40, -12, -6, 0, -44, 0, 20, -36, -164, -18, -72, 0, -42, 2, -108, -6, -30, 0, -16, -36, 0, 0, 34, 32, 0, 4, 0, 30, 0, -12, 0, 32, 84, 64, -168, 8, 0, 28, 12, -12, 0, -2, 0, -18, -268, 12, 22, 48, 0, 60, -32, 6, 102, 12, -6, 50, -36, 0, -72, 68, -8, 12, 38, 0, 18, 0, -18, -12, 52, -24, 28, 20, 88, -42, 8, 8, 6, 0, -64, 0, -48, 8, -108, 36, -6, 0, -30, 8, 150, -30, 60, -24, 0, 0, 0, -60, 2, -48, 24, -4, 0, 6, 0, -12, 50, -12, 6, 24, -44, -4, -264, -2, 32, 36, 0, -96, 0, 10, -320, -44, -16, 0, 0, -30, 48, -12, -12, 78, 30, -2, -90, 0, 24, -2, 32, 16, -20, 0, -12, 0, -36, -2, 12, -48, 28, 2, 8, -36, 12, -16, -54, 0, 40, 0, 80, 104, -12, 14, -24, 0, 24, 6, -36, 36, 24, 0, -8, 48, 0, 66, 82, -4, 84, 22, 0, 6, 0, 54, 24, -24, -18, -24, -42, -8, 12, -20, 10, 114, 0, 2, 0, -2, -44, -8, 40, -42, 0, 0, 6, -36, -108, 0, 24, -2, -114, 0, 60, 14, -8, 48, 4, 0, 64, 0, -84, 50, -6, -120, -92, 2, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 37, 5, 1, 6, 0]], "char_orbit_index": 24, "prim_orbit_index": 5, "minimal_twist": "1110.2.x.a", "char_is_minimal": true, "conrey_index": 751, "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, 0], [0, 0, 1, 0], [0, 0, 1, 0], [0, -1, 0, 1], [0, 0, 0, -1], [0, -2, 1, -2], [0, 0, 0, -1], [-1, 0, 1, 0], [1, 0, 0, 0], [2, 0, 0, 0], [-1, 0, 1, 0], [0, 1, 0, -1], [-2, 0, 4, -1], [0, -1, 0, 0], [-1, 0, 1, 0], [-2, -2, -2, 0], [0, 1, 0, -1], [0, 3, 0, -3], [0, -1, 0, 0], [-1, 2, 1, -4], [0, -2, 0, 0], [1, 0, -2, 3], [0, 1, 0, -1], [1, 0, -1, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [-1, 2, 1, -4], [1, 0, -2, 2], [0, 0, 1, 0], [2, 0, -4, 2], [0, 1, 0, -1], [0, 0, 2, 0], [0, 2, 2, 2], [2, -1, 2, 0], [-1, 0, 0, 0], [0, -3, 0, -4], [-3, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, -3, -1, -3], [-4, 1, 2, -1], [3, 0, -6, -3], [0, 0, 2, 0], [0, 0, 0, -1], [3, -1, -3, 2], [3, -2, 0, 1], [-1, 0, 0, 0], [-6, 4, 6, -8], [0, -1, 0, 1], [2, 0, -4, -2], [0, 1, 0, 0], [1, 1, -1, -2], [0, 1, 0, 0], [0, -2, 0, 2], [-4, 1, 2, -1], [0, 3, 0, 0], [2, -1, -2, 2], [-3, -1, -3, 0], [0, 0, 0, -1], [2, 11, -1, -11], [2, -2, -2, 4], [-1, 4, 0, -2], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, 0, -2], [0, -2, 0, -2], [2, 0, -4, -2], [2, -3, -1, 3], [0, -2, 1, -2], [0, 3, 6, 3], [0, 1, 0, 0], [11, 6, 0, -3], [-4, 0, 7, 0], [1, 0, 0, 0], [0, 3, 0, 0], [0, -4, 2, -4], [0, 0, -1, 0], [6, 5, -3, -5], [0, 0, 0, -1], [0, 0, -1, 0], [-3, 0, 6, 1], [3, -4, -3, 8], [-1, 4, 0, -2], [2, 4, 0, -2], [-3, -3, 3, 6], [2, -2, -1, 2], [0, 0, 0, -2], [2, 6, 2, 0], [-1, 0, 1, 0], [-2, 1, -2, 0], [2, -3, -1, 3], [4, -2, -2, 2], [1, -3, 1, 0], [-3, 0, 3, 0], [0, 1, 0, 0], [7, 0, -14, 3], [-8, 6, 4, -6], [-2, 0, 2, 0], [1, 0, 0, 0]]}