# Stored data for newform 1110.2.i.h, downloaded from the LMFDB on 25 April 2024. {"label": "1110.2.i.h", "space_label": "1110.2.i", "level": 1110, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525747180962902, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1521765413317442909, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [25, -5, 1]], [11, [-2, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+\\zeta_{6}q^{3}-\\zeta_{6}q^{4}+\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 37, "char_orbit_label": "i", "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": 6, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [1110, 3, [371, 667, 631], [3, 3, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 37], "conrey_indexes": [121, 211], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.943", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.955", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "93.333", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 1, 1, 5], "traces": [0, 2, 1, 1, -1, 1, 2, 5, -2, -1, 2, 4, 1, -5, 10, -1, -1, -2, 1, 5, 1, -5, 2, 0, -1, -1, -10, -2, 5, -18, 1, 8, 1, 2, 2, -5, 2, 1, 10, 5, -1, 8, 5, 8, -2, -2, 0, 4, -2, -18, 1, -4, -5, 8, -1, 2, -5, -5, -9, 4, 2, -14, 4, -10, 2, 5, 4, 2, 4, 0, 5, -9, 1, 32, 11, -2, 5, 10, -5, 12, -2, -1, 16, 9, 10, -4, 4, -9, -4, 0, -1, 25, 0, 4, 2, -5, -1, -8, 18, -2, 2, -4, -2, 6, 5, -10, -8, -12, 1, 14, 4, -10, -10, 13, 5, 0, 9, 10, -4, -20, 1, -14, -28, -8, -4, -2, -5, -5, 1, 4, -5, -18, 2, -25, 4, -1, 2, -6, 0, -12, 10, 2, -18, -10, -1, -9, 16, -36, 10, 30, -1, 6, -5, -2, 20, 4, -10, 13, 24, 16, -1, 0, -2, 2, 8, -2, -9, -18, 5, -12, -2, -10, -4, 0, -18, -10, -2, 8, 0, -24, 1, 14, -25, 14, 0, -10, 8, -4, -2, -5, 5, 8, 1, -32, -4, 10, 36, 24, 2, 28, 1, -2, -2, -45, 2, -8, 3, 0, 10, 10, -5, -34, -16, 9, -24, 4, 2, 20, -14, 16, 2, 20, 1, 24, -5, -1, -13, -25, 10, 4, 0, -10, 18, -6, 5, 2, -8, -12, -10, 27, -1, -18, -7, 1, -14, -36, 8, 25, -8, 18, -1, 28, 5, 0, 5, -2, -1, 13, 8, -50, -10, 9, 18, 0, -2, 16, 25, 0, 2, -30, -2, -20, -2, 50, -3, -2, 0, 1, 12, -4, 5, 18, 4, -6, -9, -10, -20, -40, -2, 13, -18, -4, -16, -24, -18, 8, -1, -4, 15, 0, 1, 20, 12, -2, -10, 14, -4, -4, 10, 3, 8, 24, -5, 0, -13, -5, 12, -32, 8, -36, 1, 12, 0, -20, -1, 10, -2, 28, -8, 10, 2, -7, -18, -11, -36, -2, -5, 14, 12, 26, 2, 16, -5, -110, -8, 0, 0, -34, -9, 20, -5, 5, 2, -5, 4, 9, 0, -10, -12, 34, 2, -6, 28, -7, -50, 16, -14, -17, 0, -16, 1, 80, 4, -3, 4, -1, -4, 45, -10, 13, 10, -10, 4, -6, 2, -10, -16, -4, 4, 21, 5, 0, 18, -36, -24, -12, 4, -4, 14, -50, -1, -60, 2, -20, 2, 1, -90, 2, 4, -3, 8, -3, -3, 40, 0, 18, 5, -24, 20, -34, 5, -16, -17, -2, -8, -2, -9, 70, -12, 10, 8, 13, 1, 76, 40, 9, -28, 0, 32, -22, -2, -18, 10, -6, 11, 0, 12, 15, 5, -20, -2, 16, -26, -6, -50, 50, 5, 38, 8, 2, 0, -35, 10, -23, 9, -4, -3, 78, -5, -10, 4, 26, -4, 16, 12, -10, 10, 8, -27, -12, -2, 50, -36, 0, 7, -4, -1, 66, 14, 4, -18, 12, 16, 18, -25, -4, -4, 45, 9, 31, 1, 18, 14, -12, 10, -2, 0, -24, 10, 9, -4, 80, -2, -5, -13, 3, 4, 8, 5, 0, -5, 6, -9, -42, 36, -5, 0, -8, -4, -46, 8, 4, 50, 40, 0, 12, -2, -12, -15, -36, -1, 76, 20, -14, -4, 28, 25, 80, 3, 28, 2, -45, 0, -60, 2, -11, 24, -14, 4, -20, -5, -8, -18, -22, 2, 26, -12, 5, 9, 24, -5, 19, -10, 4, 40, 0, -1, -26, 26, -16, -9, 90, -8, 16, -32, 5, -48, -7, 18, 20, 4, 48, -11, 36, -2, -10, -15, 14, 0, 17, 2, -34, 40, -4, 6, -7, -4, 1, -5, 45, -14, -10, -2, 15, -2, -16, -10, -25, 6, -8, 4, 0, -24, 0, 5, -1, 0, -10, -26, -22, -10, -32, -12, -17, 32, -10, -8, 180, -18, 18, 2, -42, -12, 52, 0, -4, -10, -26, 1, 8, 5, -20, -4, -28, 14, -36, -16, -16, 20, 48, 4, -32, 7, 10, -9, -50, -10, 0, -18, 12, 2, -28, -10, 8, 28, 1, 24, -12, 13, -20, 4, 25, 8, -36, 5, -3, -55, -4, -4, -80, 0, 45, 0, -20, -17, -24, 9, -32, -20, -3, 5, -30, 10, -50, 4, -2, 5, -10, -4, 76, -9, -24, 0, 0, -20, 10, 12, 54, 17, 43, 1, 15, 6, 18, 14, 9, -14, -35, -25, 2, 32, -8, -28, -30, -34, -18, 0, 4, -8, 34, 11, 50, 40, 36, -4, 15, -6, 9, 8, 60, -2, -92, -2, 14, 90, -6, -5, 13, -13, 0, 5, -8, -5, 140, -4, 2, -12, -40, 1, -82, 10, 26, 16, 48, 4, -4, 8, -55, 42, -40, -5, -18, 0, 18, -18, 26, -18, 0, -48, 0, 12, 130, 2, -70, -2, 8, -14, 24, -25, -4, -2, 0, -30, 64, 4, 0, -40, -15, 4, 48, -1, -40, -45, -40, 22, 4, 2, 20, 3, 25, 16, 5, -6, -41, -6, -4, 20, -15, 0, -40, 9, -1, -5, -36, -12, 18, 10, -8, 34, -4, 10, 104, -8, 36, 17, -24, 2, -35, 8, 6, -4, 0, -18, 26, -70, -5, 12, -82, -10, -78, 4, -80, 26, 0, -1, 0, 38, -13, 20, 24, -9, 10, -14, 4, 0, -5, 16, -26, -44, 24, -4, 18, -36, 2, -10, 4, -3, -40, 10, -50, 0, -2, -12, 10, 30, -12, 10, 0, -40, -72, -1, 16, 32, -20, -13, -14, 6, 32, -25, 2, 25, -54, -5, 18, 76, 28, 4, -180, -2, -64, 0, -2, 35, -45, 20, -11, -46, -3, -9, 18, 4, -180, 3, 48, 39, -8, -10, -8, 10, 0, 2, -35, 13, 0, 4, 5, 8, -43, 24, -80, -5, -64, 20, 3, 16, 4, -54, -18, 12, -15, -1, -30, -5, 24, -18, -16, 0, -1, 14, -10, -8, 32, -2, -120, 33, 5, 28, 13, 2, 0, 18, 14, 6, -6, 8, 48, -18, -10, -50, 0, -2, 8, 4, -14, -45, 14, -9, -3, 62, -1, 2, 50, -18, 8, -14, -4, 12, 80, 5, 58, -4, -14, 0, -36, -12, 45, 5, 13, -9, -4, -2, 14, 160, 8, -1, -16, -10, 60, -26, -55, 6, -8, -4, 36, 4, 0, 55, 56, 0, -42, 5, -17, 12, 75, -18, -10, -84, 40, 18, 10, -10, -21, 0, -5, 8, -17, -2, -30, -23, -10, -8, 6, 8, -66, 25, 18, -40, -16, 0, 0, -12, 10, -4, -9, -24, -4, 15, 17, 36, -90, 1, 0, 38, -12, 40, -20, 14, 26, -2, 7, 14, 16, -25, -11, 40, -16, 6, 54, 14, 130, 4, 17, -90, -6, 0, 10, 60, -8, 1, 20, -10, -8, 12, 40, 14, 12, 8, 19, -40, 3, -10, 40, -4, -52, -36, 1, -11, 0, -2, -59, 13, -45, -6, 12, -5, 25, 18, 26, 12, -8, 5, 20, -19, -5, 10, -4, 8, 4, 80, 6, 0, 24, 1, 32, 26, -20, 13, 0, -32, 70, 9, -8, 45, 11, -4, -3, -16, -21, -16, 90, 10, -13, -24, 0, -14, -2, 36, -24, 40, -18, -4, 14, 24, -120, -10, -24, 18, -27, 2, -72, -20, -2, -30, 45, 28, 54, 0, -25, 34, 28, 1, -61, 34, -30, 20, 18, -2, 36, -6, 20, -14, 0, -2, -4, -1, 2, 5, -14, -45, 0, -28, -20, -20, -14, 2, -18, -15, -6, 2, 28, -8, -8, -20, 3, 25, 50, 3, 7, -4, 20, -4, -32, 0, 26, -48, 9, 0, -72, 10, 10, -2, -12, 0, -60, 10, 14, -13, -68, -20, -72, -5, 20, 32, -8, -24, 0, -34, -70, 64, -4, -5, 32, -16, -10, 90, 2, 18, -36, 9, -2, 1, 140, 42, -36, -24, 26, 26, 20, 0, -96, 4, -3, 10, -13, -52, -55, 2, -62, -8, 38, -5, -46, 20, 48, -2, 18, -56, 43, -14, -40, -18, 0, -8, 10, 16, 0, 10, 22, 96, 45, 2, 110, -64, 18, 14, 8, 20, -8, 9, -3, -25, -72, 1, 32, 0, 0, 18, 20, 24, -15, 4, -15, -56, -48, -5, -15, 16, 20, 14, 45, -1, -80, 12, -16, -6, -40, -13, 0, -40, -12, 2, -140, -25, -36, -8, 25, 36, 66, 10, -73, -6, -38, 55, -26, 4, -4, 4, 4, -40, 240, 0, 58, -45, -70, 0, -1, -10, 80, 17, 23, -12, -60, 18, 70, -16, -8, -40, -10, -6, 50, 10, 39, 30, 0, 5, 36, 5, -20, 2, 30, 2, 18, 10, 13, -20, 6, -8, -140, 38, 8, -18, 162, -12, -55, 0, -5, 0, -32, -10, -48, -10, -8, 24, -132, 27, -80, -17, -24, -43, 65, -1, -36, 30, 55, 12, -13, -18, -53, -14, 0, -9, 96, -7, -118, -70, 4, 25, 16, 1, -39, 16, 33, 8, -50, -14, 24, -60, 2, -17, -130, -36, 44, 0, 6, 8, 4, 8, -85, 17, 36, 10, -92, 25, 44, -40, -2, 72, -18, -8, 65, 30, 90, -3, 8, 18, 0, 4, -31, -60, 46, -1, -60, -46, 36, 2, -20, 28, -12, 45, -24, 6, -78, 5, 0, -13, 2, -26, -80, 0, -72, -5, -12, 8, 24, 5, 28, 70, 18, -8, -24, -2, 30, -6, -80, -20, -2, -1, -72, -41, 5, 20, 0, 13, 104, 32, -3, 96, 50, 8, 22, 4, 4, 4, -102, -50, 48, 21, 0, 40, 3, -10, 60, -36, -6, 0, 0, 9, 0, -36, 42, 13, 64, 18, 35, 0, 5, -24, 90, 0, -5, 24, -16, 65, 108, -2, -64, 70, -23, 2, 125, 16, 4, -28, -4, -24, -18, 25, 100, 4, 80, -1, -104, 0, -20, 30, 24, 32, -18, 2, 54, 0, 12, -20, 46, -30, -10, 2, -72, 96, 56, -2, -38, -80, 38, 45, 5, -20, -92, 20, -28, 2, -15, -2, 0, 40, 14, 6, 8, 50, 60, 8, 40, 10, 32, -3, -10, 41, 14, -3, 8, -2, 50, -20, 45, -30, -14, 0, -12, 40, -120, -9, 12, 1, -8, -10, -1, -72, 3, 12, -6, -18, -28, -10, 270, -4, -4, 68, 20, 4, 0, 5, -23, 52, -4, 8, -14, 18, 90, 34, -11, -12, 0, 4, -46, -70, 13, 16, 27, -6, 39, -2, 10, 0, 180, -9, 8, -26, 12, -140, -61, -10, -36, 24, 38, -41, -55, -20, 4, -39, -4, -4, 0, -40, 46, 13, 0, 0, 26, -2, 250, 0, -52, -38, 40, 13, -17, -20, 16, 48, 2, -18, 32, -10, 45, 14, 40, -4, 44, 0, 32, -10, -6, -16, 20, -13, -5, -22, 70, -24, 74, -2, 7, 36, 32, -18, -10, 4, -20, -20, 126, 8, 0, 3, 24, -20, 18, -1, -60, -25, 18, 0, 15, -4, 40, -24, 10, 20, -62, 15, -48, -24, -14, 5, 4, 0, 17, -20, -17, -36, 130, 1, 31, 32, -68, 16, -12, 20, 120, 13, -2, 14, 16, 12, -198, 64, 7, 25, 0, -2, 48, -25, 2, -27, -12, -10, -16, -18, 90, 38, 16, 14, -16, -4, 10, -90, 17, -4, -36, -32, 30, 0, 0, -4, -20, 70, -8, 45, 0, 10, -54, -10, -50, -23, 28, 3, 40, -18, -4, 36, -24, 8, -128, -90, 0, 6, 3, 24, 66, -39, 0, -4, -48, -5, -56, 8, 1, 20, -4, 0, 112, -2, -20, 35, -75, -13, -45, 0, -2, 8, 18, -5, -56, -8, -64, 43, 26, 12, -200, -160, 17, 5, -22, -32, 0, 10, -5, -3, -27, 8, 0, 8, 90, -27, 52, -36, 6, 24, 9, -30, -10, 1, 26, -15, -84, -55, -20, 12, 16, 18, 26, -32, -60, 0, 27, -2, -8, 7, -75, -20, -5, -4, 26, -32, -18, -1, -21, -60, 16, -33, 17, 10, -72, 14, -40, -13, 0, -2, 15, 0, 28, 36, 88, 28, 30, -6, -18, 6, 180, -8, -48, 24, -32, -36, -56, 10, -24, -25, -48, 0, 64, 2, 30, 4, 32, 8, -2, -7, 12, -90, -10, 28, 28, -18, -4, 3, -25, 31, 96, -11, -144, 1], "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, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "1110.2.i.h", "char_is_minimal": true, "conrey_index": 121, "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], [1, 0], [1, -1], [0, 1], [0, -1], [0, 1], [1, 0], [0, 5], [-1, 0], [-1, 1], [1, 0], [2, 0], [1, -1], [0, -5], [5, 0], [-1, 1], [-1, 1], [-2, 2], [0, 1], [0, 5], [1, -1], [-5, 5], [2, -2], [0, 0], [0, -1], [-1, 1], [-5, 0], [-1, 0], [5, -5], [-9, 0], [0, 1], [4, 0], [0, 1], [0, 2], [0, 2], [-5, 5], [1, 0], [-3, 7], [5, 0], [5, -5], [0, -1], [0, 8], [0, 5], [4, 0], [0, -2], [-1, 0], [0, 0], [2, 0], [-1, 0], [-18, 18], [0, 1], [-2, 0], [-5, 5], [8, -8], [-1, 1], [0, 2], [0, -5], [-5, 5], [-9, 9], [4, -4], [1, 0], [0, -14], [4, -4], [-5, 0], [1, 0], [5, -5], [2, 0], [0, 2], [2, 0], [0, 0], [0, 5], [0, -9], [1, -1], [16, 0], [4, 3], [-1, 0], [5, -5], [0, 10], [0, -5], [0, 12], [-1, 0], [0, -1], [8, 0], [9, -9], [5, 0], [-2, 0], [4, -4], [0, -9], [-2, 0], [0, 0], [-1, 1], [25, -25], [0, 0], [0, 4], [2, -2], [-5, 5], [-1, 1], [-4, 0], [0, 18], [-2, 2], [1, 0]]}