# Stored data for newform 1110.2.h.f, downloaded from the LMFDB on 07 March 2021.
{"level_primes": [2, 3, 5, 37], "is_polredabs": true, "sato_tate_group": "1.2.3.c2", "rm_discs": [], "conrey_indexes": [961], "cm_discs": [], "trace_hash": 1052710254287224126, "level_radical": 1110, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 2, "is_cm": false, "hecke_orbit": 6, "analytic_conductor": 8.863394624362122, "inner_twist_count": 2, "field_disc_factorization": [[-1, 1], [2, 6], [2089, 2]], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": 1, "label": "1110.2.h.f", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "1110.2.h.f", "field_poly_is_cyclotomic": false, "dim": 6, "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 6, 0, 6, -6, 0, 0, -6, 0, 6, -6, 6, -6, 0, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, -6, 18, 6, 6, 0, -6, 0, 0, 6, 10, 0, -6, -2, -18, 0, 6, -12, 0, 0, -6, 0, -2, -24, 6, 16, 0, 0, 0, 6, 0, 0, 0, 0, 12, 0, 0, 0, -8, -6, -6, 18, 0, 0, 0, 0, 6, -20, 0, -26, -4, -6, 0, 46, 18, 0, 0, 6, 0, 14, 6, 10, -4, 0, 0, 0, -6, 0, 0, 0, 0, -18, 0, 0, 0, 6, 6, 8, 10, 0, -18, 0, 0, 50, -6, 0, -6, -2, -6, 0, -18, -2, 0, 0, -16, 0, 6, -8, 12, -12, 0, 0, 0, -66, 0, 0, 0, 0, -6, 0, 0, 0, -10, -20, -2, -48, 0, -24, 0, 0, 6, 12, 0, 16, 2, 8, 0, 86, 18, 0, 0, -8, 0, 20, -40, 6, -6, 0, 0, 0, 12, 0, 0, 0, 0, -28, 0, 0, 0, 22, 12, 6, 6, 0, -30, 0, 0, 44, 34, 0, 2, -4, -8, 0, 24, -6, 0, 0, -6, 0, -24, 18, -16, -78, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 6, -36, -6, -20, 0, -4, 0, 0, 50, -26, 0, -54, -4, 52, 0, -6, -12, 0, 0, 56, 0, 46, -12, -28, 18, 0, 0, 0, 14, 0, 0, 0, 0, 6, 0, 0, 0, 106, 8, 14, 6, 0, 6, 0, 0, 10, 6, 0, -4, -36, -18, 0, 8, 16, 0, 0, -34, 0, 0, -78, -6, 16, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 20, -18, 70, 12, 0, -140, 0, 0, 26, -18, 0, -16, 4, 6, 0, -18, 6, 0, 0, 8, 0, 12, 10, 40, -46, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 50, 26, 54, -6, 0, -42, 0, 0, 128, -6, 0, -14, -2, 2, 0, -6, -18, 0, 0, -10, 0, -18, -54, 4, -2, 0, 0, 0, -76, 0, 0, 0, 0, -16, 0, 0, 0, 68, 28, 6, 8, 0, -8, 0, 0, 12, 10, 0, -12, 2, 46, 0, 44, 34, 0, 0, -36, 0, 84, 18, -66, -74, 0, 0, 0, 48, 0, 0, 0, 0, -222, 0, 0, 0, -40, -6, -28, 80, 0, -6, 0, 0, 52, -8, 0, -12, -40, -10, 0, 12, -20, 0, 0, -2, 0, 18, -48, -70, 70, 0, 0, 0, -24, 0, 0, 0, 0, -50, 0, 0, 0, 6, -26, -20, 12, 0, 18, 0, 0, 6, 16, 0, -8, 2, -30, 0, 8, 6, 0, 0, -12, 0, 86, 8, 34, 18, 0, 0, 0, 2, 0, 0, 0, 0, -8, 0, 0, 0, 208, 24, 20, 16, 0, -40, 0, 0, 6, -56, 0, -6, 78, -80, 0, 8, -24, 0, 0, -12, 0, -16, -6, 12, -20, 0, 0, 0, -28, 0, 0, 0, 0, 20, 0, 0, 0, 22, -28, 66, -14, 0, -54, 0, 0, 98, -16, 0, 80, -62, 22, 0, 164, 12, 0, 0, 6, 0, -188, 6, -88, -6, 0, 0, 0, -30, 0, 0, 0, 0, -64, 0, 0, 0, 44, 10, 50, 34, 0, 20, 0, 0, 36, 2, 0, 26, -4, 48, 0, -8, 88, 0, 0, -18, 0, 24, -12, -58, -6, 0, 0, 0, -144, 0, 0, 0, 0, -6, 0, 0, 0, -12, 66, -24, 58, 0, 18, 0, 0, -16, -52, 0, -78, -2, 104, 0, 14, -8, 0, 0, 36, 0, -58, -72, 0, -86, 0, 0, 0, -18, 0, 0, 0, 0, -20, 0, 0, 0, 8, -16, -24, 8, 0, 120, 0, 0, 6, 28, 0, -20, -70, 6, 0, 40, -36, 0, 0, -6, 0, 12, -20, 6, -104, 0, 0, 0, -4, 0, 0, 0, 0, -18, 0, 0, 0, 50, 8, -12, -26, 0, -36, 0, 0, 148, -54, 0, -34, -4, 4, 0, 52, 0, 0, 0, -46, 0, -6, 28, 22, -12, 0, 0, 0, -36, 0, 0, 0, 0, 56, 0, 0, 0, 68, -22, 46, -36, 0, -12, 0, 0, -28, -6, 0, 18, -78, -6, 0, -28, 124, 0, 0, 20, 0, 30, -204, 14, 70, 0, 0, 0, -112, 0, 0, 0, 0, -44, 0, 0, 0, -34, 6, 26, 256, 0, -72, 0, 0, -2, 208, 0, 8, 4, 106, 0, 28, 8, 0, 0, 14, 0, -282, 6, 96, -24, 0, 0, 0, 6, 0, 0, 0, 0, -164, 0, 0, 0, 10, -6, 124, 6, 0, -46, 0, 0, 210, -4, 0, 24, -36, 128, 0, -18, -68, 0, 0, 16, 0, 8, -20, 78, 16, 0, 0, 0, -36, 0, 0, 0, 0, -34, 0, 0, 0, 106, -106, 0, 26, 0, -78, 0, 0, -6, 36, 0, 16, -70, -42, 0, -88, 64, 0, 0, -82, 0, -18, 16, -6, -60, 0, 0, 0, -14, 0, 0, 0, 0, 2, 0, 0, 0, 184, -6, 150, 20, 0, 36, 0, 0, 136, 6, 0, -10, -78, 20, 0, -12, -18, 0, 0, 70, 0, 4, 12, -82, -144, 0, 0, 0, -140, 0, 0, 0, 0, -50, 0, 0, 0, 26, -12, -40, -18, 0, 4, 0, 0, 54, -16, 0, -48, 4, 14, 0, 6, -52, 0, 0, 68, 0, -18, 8, 16, 6, 0, 0, 0, 12, 0, 0, 0, 0, 8, 0, 0, 0, 94, -44, 12, -56, 0, 10, 0, 0, 40, -48, 0, -46, 2, -12, 0, 12, 112, 0, 0, 28, 0, -80, 34, -18, -228, 0, 0, 0, 72, 0, 0, 0, 0, -80, 0, 0, 0, 18, 0, -14, 84, 0, -74, 0, 0, -78, -8, 0, -54, -44, 50, 0, 48, 26, 0, 0, 54, 0, -292, -6, -160, -40, 0, 0, 0, -42, 0, 0, 0, 0, -32, 0, 0, 0, 128, -106, 248, -6, 0, -8, 0, 0, 80, -14, 0, 38, -2, -6, 0, 2, 276, 0, 0, 16, 0, -6, 20, -8, -18, 0, 0, 0, -12, 0, 0, 0, 0, -10, 0, 0, 0, -6, 12, -18, 92, 0, -54, 0, 0, 4, 114, 0, -2, 36, -20, 0, 30, 18, 0, 0, -84, 0, -70, -12, -76, -8, 0, 0, 0, -16, 0, 0, 0, 0, -6, 0, 0, 0, -134, -16, 20, 34, 0, -36, 0, 0, 116, -50, 0, 0, 8, 68, 0, 78, 28, 0, 0, 6, 0, -98, 8, -16, -20, 0, 0, 0, -8, 0, 0, 0, 0, 62, 0, 0, 0, 12, -96, 6, 10, 0, 52, 0, 0, 68, -12, 0, 126, 2, 140, 0, 46, -12, 0, 0, 84, 0, 44, 6, -124, 34, 0, 0, 0, -28, 0, 0, 0, 0, -36, 0, 0, 0, 8, -20, 84, 110, 0, 18, 0, 0, -66, -70, 0, -74, -148, -12, 0, 2, 156, 0, 0, 136, 0, 140, -66, 48, 36, 0, 0, 0, -136, 0, 0, 0, 0, -26, 0, 0, 0, 18, -222, 68, 24, 0, -182, 0, 0, 16, -6, 0, -308, -4, -40, 0, 120, -6, 0, 0, -28, 0, -136, 80, -56, 18, 0, 0, 0, -6, 0, 0, 0, 0, -80, 0, 0, 0, 52, 8, 86, -8, 0, -64, 0, 0, 76, -12, 0, -12, -40, 32, 0, -10, -16, 0, 0, -40, 0, 12, 154, 46, -20, 0, 0, 0, 28, 0, 0, 0, 0, -2, 0, 0, 0, 186, 8, 18, 68, 0, -48, 0, 0, -70, 20, 0, 70, -128, -204, 0, 176, -20, 0, 0, 22, 0, -100, 0, -24, 66, 0, 0, 0, -32, 0, 0, 0, 0, -130, 0, 0, 0, -26, -50, 98, 66, 0, -26, 0, 0, 20, -54, 0, -22, -62, 6, 0, -92, -26, 0, 0, -20, 0, 42, 12, -172, -94, 0, 0, 0, 18, 0, 0, 0, 0, -128, 0, 0, 0, 6, -238, 34, 16, 0, -6, 0, 0, 14, -8, 0, 54, 2, 168, 0, -30, -2, 0, 0, 104, 0, 8, 12, 268, 6, 0, 0, 0, 18, 0, 0, 0, 0, -12, 0, 0, 0, 244, -80, 86, 10, 0, 8, 0, 0, 34, -16, 0, 18, -58, 20, 0, 54, 182, 0, 0, -4, 0, 70, 26, 2, -140, 0, 0, 0, 26, 0, 0, 0, 0, 48, 0, 0, 0, -20, -8, 76, -118, 0, -170, 0, 0, 104, 4, 0, -18, 44, 208, 0, -20, 24, 0, 0, 20, 0, -58, 16, -22, -82, 0, 0, 0, -40, 0, 0, 0, 0, -216, 0, 0, 0, 6, -68, 264, -56, 0, -28, 0, 0, 116, -6, 0, -40, 78, -8, 0, -80, 268, 0, 0, -12, 0, 8, -136, 76, -24, 0, 0, 0, -84, 0, 0, 0, 0, -12, 0, 0, 0, -10, 36, -16, -6, 0, -6, 0, 0, 12, -68, 0, -20, -2, -44, 0, 84, -46, 0, 0, -16, 0, -14, -8, -28, -44, 0, 0, 0, -34, 0, 0, 0, 0, -92, 0, 0, 0, -72, 20, -48, 36, 0, -86, 0, 0, -22, 70, 0, -84, 4, 22, 0, -18, -28, 0, 0, 66, 0, -178, -14, 74, -256, 0, 0, 0, -54, 0, 0, 0, 0, -20, 0, 0, 0, 98, -146, -48, -16, 0, -330, 0, 0, 8, 80, 0, -24, -62, 120, 0, 22, 36, 0, 0, 128, 0, 164, 222, 28, 12, 0, 0, 0, -20, 0, 0, 0, 0, 6, 0, 0, 0, 188, 40, -188, 12, 0, 6, 0, 0, -88, 28, 0, -6, 8, -80, 0, 32, 12, 0, 0, 8, 0, 6, 224, -30, -8, 0, 0, 0, 316, 0, 0, 0, 0, -52, 0, 0, 0, 8, -64, -174, -68, 0, 48, 0, 0, 12, -18, 0, 124, 40, 44, 0, 56, 10, 0, 0, 50, 0, -98, 34, -68, -12, 0, 0, 0, 20, 0, 0, 0, 0, 88, 0, 0, 0, 36, -20, 148, 2, 0, -50, 0, 0, 166, 26, 0, -18, -4, 204, 0, 48, -204, 0, 0, 70, 0, -8, 0, -70, 88, 0, 0, 0, -222, 0, 0, 0, 0, -18, 0, 0, 0, 28, 66, 24, 228, 0, -12, 0, 0, -58, -96, 0, -6, -124, -156, 0, -36, 166, 0, 0, 50, 0, 32, 50, -144, -18, 0, 0, 0, 26, 0, 0, 0, 0, 116, 0, 0, 0, -56, -6, 230, -22, 0, 26, 0, 0, -36, 20, 0, -12, -68, -12, 0, 208, 66, 0, 0, -24, 0, -18, 58, -6, -376, 0, 0, 0, 18, 0, 0, 0, 0, -6, 0, 0, 0, -16, -28, 70, -52, 0, -24, 0, 0, 8, -78, 0, 20, -2, 182, 0, 104, 30, 0, 0, -2, 0, 14, -32, 34, -8, 0, 0, 0, -6, 0, 0, 0, 0, 36, 0, 0, 0, 90, 34, -58, 12, 0, -72, 0, 0, 0, -44, 0, -86, -54, 58, 0, -8, 188, 0, 0, -34, 0, -144, -100, -18, 26, 0, 0, 0, 152, 0, 0, 0, 0, 124, 0, 0, 0, 28, -20, -2, 144, 0, -176, 0, 0, -108, 40, 0, -70, 4, 8, 0, 190, -16, 0, 0, -24, 0, -364, 8, 84, 32, 0, 0, 0, 120, 0, 0, 0, 0, -28, 0, 0, 0, 6, -208, 88, 28, 0, -24, 0, 0, 130, -20, 0, 4, -70, -16, 0, 6, 16, 0, 0, 96, 0, 40, 248, -158, -36, 0, 0, 0, 130, 0, 0, 0, 0, -6, 0, 0, 0, 56, -308, 12, -6, 0, -20, 0, 0, 6, 20, 0, -104, -78, -46, 0, 48, 80, 0, 0, -18, 0, -68, -80, -4, -8, 0, 0, 0, 24, 0, 0, 0, 0, 128, 0, 0, 0, -112, -18, -178, 12, 0, -242, 0, 0, -104, 126, 0, 16, -40, 50, 0, 6, 8, 0, 0, -12, 0, 78, -26, 20, -426, 0, 0, 0, -36, 0, 0, 0, 0, 64, 0, 0, 0, 148, -388, 28, -54, 0, -12, 0, 0, 214, -34, 0, 8, -4, -120, 0], "hecke_ring_index_factorization": [[2, 1]], "nf_label": "6.0.279290944.1", "field_poly": [16, 0, 169, 0, 26, 0, 1], "has_non_self_twist": 1, "char_values": [1110, 2, [371, 667, 631], [2, 2, 1]], "Nk2": 4440, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "h", "weight": 2, "trace_display": [0, 6, 0, -6], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 2, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+\\beta _{2}q^{2}+q^{3}-q^{4}+\\beta _{2}q^{5}+\\beta _{2}q^{6}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": -279290944, "level_is_prime_power": false, "relative_dim": 6, "hecke_cutters": [[7, [-16, -10, 3, 1]], [13, [64, 0, 340, 0, 53, 0, 1]]], "space_label": "1110.2.h", "level": 1110, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 37, 2, 1, 2, 0]], "char_degree": 1, "char_conductor": 37, "char_orbit_index": 8, "hecke_ring_generator_nbound": 37, "hecke_orbit_code": 22518479206745174, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.858", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "184.232", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8760.111", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0], [-1, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 1, -3, 0, 0, 0], [0, -1, -1, 0, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, -1, 0, 1, 1], [0, 0, 1, 0, 0, 0], [0, -1, 3, 0, 0, 0], [0, 0, -1, 0, 0, 0], [-1, 0, 0, 1, 0, 0], [0, -1, 1, 0, 0, 0], [0, 1, 1, 0, 1, 1], [0, 0, -1, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [3, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0], [0, 0, -2, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 2, 0, 1, 1], [0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [1, 0, 0, 1, -1, 1], [0, -1, -1, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -1, 1, -1, 1, 0], [-3, 0, 0, -1, 0, 0], [0, 1, -3, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 0], [0, -2, 0, 0, -1, -1], [-1, 0, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0], [-1, 0, 0, 1, -1, 1], [-4, 0, 0, 2, 0, 0], [1, 0, 0, 0, 0, 0], [2, 0, 0, -1, -1, 1], [0, 0, -1, 0, 0, 0], [0, 1, -1, 0, 1, 1], [0, -1, 3, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, -1, 3, 0, 0, 0], [2, 0, 0, 0, 0, 0], [0, -2, 2, 0, -1, -1], [0, 0, -1, 0, 0, 0], [0, 0, -2, 0, 0, 0], [-2, 0, 0, 0, -1, 1], [-1, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, 0], [3, 0, 0, 1, 0, 0], [0, -1, 1, 0, 0, 0], [0, 0, 0, 4, 0, 0], [0, -1, 1, 0, -1, -1], [0, 1, 1, 0, 1, 1], [1, 0, 0, -1, 0, 0], [-2, 0, 0, -2, 2, -2], [0, 0, -1, 0, 0, 0], [-5, 0, 0, -1, -1, 1], [-1, 1, 0, -1, 0, 1], [-1, 0, 0, 0, 0, 0], [0, 1, -3, 0, 0, 0], [7, 0, 0, 1, -1, 1], [3, 0, 0, 1, 0, 0], [0, 0, 6, 0, -1, -1], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0], [3, 0, 0, 1, 1, -1], [1, 0, 0, -1, 0, 0], [1, 0, 0, 1, -1, 1], [0, 0, 0, -2, 1, -1], [0, 0, -2, 0, 0, 0], [0, 1, -1, 0, 0, 0], [0, 3, 5, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 3, -5, 0, 1, 1], [0, -1, -1, 0, -1, -1], [0, 0, 2, 0, 1, 1], [0, -2, -4, 0, 0, 0], [-3, 0, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0], [0, -2, 4, 0, 0, 0], [0, 1, 2, 0, -1, -1], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]]}