# Stored data for newform 1110.2.u.d, downloaded from the LMFDB on 24 April 2024. {"label": "1110.2.u.d", "space_label": "1110.2.u", "level": 1110, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13512173305201750, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 188595507862129391, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [-2, 1]]], "qexp_display": "q-\\zeta_{8}^{3}q^{2}+(\\zeta_{8}+\\zeta_{8}^{2}-\\zeta_{8}^{3})q^{3}-\\zeta_{8}^{2}q^{4}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 111, "char_orbit_label": "u", "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": 8, "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": "0.633", "prec": 17}, "analytic_rank_proved": true, "char_values": [1110, 4, [371, 667, 631], [2, 4, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 3, 5, 37], "conrey_indexes": [191, 401], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.079", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "102.100", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3566.176", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 8], "traces": [0, 4, 0, 0, 0, 0, 4, 8, 0, 4, 4, 0, 4, 4, 0, 4, -4, 0, 8, -12, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -28, 0, 0, 24, 0, 0, -4, 0, 4, 0, 0, 8, 28, 0, -8, -16, 0, 0, -12, 0, 24, -4, 0, -4, 0, 0, -12, 0, 0, 4, -36, 0, 8, 0, 0, 0, 0, 0, -16, 8, 0, 8, 0, 0, -4, 12, 0, 0, 12, 0, -28, 16, 0, 8, 0, 0, 24, 0, 0, 4, 8, 0, 28, -8, 0, -4, 28, 0, 0, 4, 0, 0, -20, 0, 8, 16, 0, 20, -12, 0, -24, -8, 0, 0, 0, 0, 4, 32, 0, 4, -44, 0, 32, -28, 0, 16, -64, 0, 28, 4, 0, 0, -24, 0, -4, 0, 0, 0, 0, 0, 0, 8, 0, -4, 24, 0, 0, 24, 0, 4, 0, 0, -48, 0, 0, 4, -16, 0, 0, -4, 0, 16, -60, 0, 0, 8, 0, -8, 0, 0, -12, -28, 0, 24, 0, 0, 32, 0, 0, 8, 0, 0, 36, 0, 0, -56, 0, 0, 0, -12, 0, -4, -4, 0, 8, 0, 0, 0, 4, 0, -16, -8, 0, 24, 16, 0, 32, -4, 0, 0, 80, 0, 0, -32, 0, 4, -56, 0, 24, 0, 0, 20, -96, 0, 0, 0, 0, -12, -104, 0, 0, -24, 0, 16, 8, 0, 12, 48, 0, -4, -44, 0, 0, -36, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, -24, 4, 0, 0, -8, 0, 48, 0, 0, 0, -16, 0, -8, 16, 0, 0, 40, 0, 8, 8, 0, -16, 44, 0, -28, 0, 0, 8, 12, 0, -24, 0, 0, -8, 0, 0, 28, -24, 0, -12, 0, 0, 0, -56, 0, 0, 56, 0, -16, 12, 0, 24, 0, 0, 20, -28, 0, -8, 4, 0, -16, -12, 0, -16, 0, 0, 0, -32, 0, 0, 4, 0, -12, -16, 0, 0, 60, 0, -4, 64, 0, 0, 0, 0, -8, 24, 0, -48, -80, 0, 16, 0, 0, -24, 128, 0, 20, 0, 0, 0, -8, 0, 48, 0, 0, 0, 0, 0, 0, -8, 0, -72, 128, 0, 0, -4, 0, -28, 0, 0, -4, -8, 0, -8, -24, 0, 0, -32, 0, 4, 0, 0, 28, -28, 0, 4, 0, 0, -64, 8, 0, 0, 0, 0, -24, 0, 0, 16, -56, 0, -16, 0, 0, 24, -20, 0, 0, -20, 0, -16, -8, 0, -16, 0, 0, 8, 36, 0, 32, 16, 0, -8, -72, 0, 0, 28, 0, 0, -96, 0, 0, 12, 0, -24, 108, 0, -12, 24, 0, -4, -8, 0, 0, 0, 0, -8, 0, 0, 72, -96, 0, 24, -28, 0, -24, -16, 0, 0, 44, 0, 0, 80, 0, -4, 0, 0, 0, 0, 0, 0, -12, 0, -64, 80, 0, 0, 20, 0, -32, 0, 0, -44, 68, 0, 60, -12, 0, 0, 144, 0, 0, 28, 0, -8, 12, 0, 64, 0, 0, 16, -8, 0, -44, 0, 0, 24, 0, 0, -60, -56, 0, 28, 0, 0, 0, -4, 0, 0, 12, 0, -8, -88, 0, 0, 0, 0, -64, 24, 0, -8, 32, 0, 64, 56, 0, -4, 84, 0, 0, -24, 0, 0, 28, 0, -36, 0, 0, -16, 24, 0, -28, 16, 0, 0, 0, 0, 0, 72, 0, -16, -8, 0, -56, 8, 0, -12, 120, 0, -32, 32, 0, 0, 108, 0, -4, 0, 0, 0, 0, 0, 0, -64, 0, -12, 168, 0, 0, 4, 0, 0, 0, 0, -4, -16, 0, 4, 48, 0, 0, -72, 0, -8, -36, 0, 48, -36, 0, 48, 0, 0, -16, 0, 0, -40, 0, 0, 16, 0, 0, -4, -4, 0, 0, 0, 0, 8, -76, 0, 0, 0, 0, 32, -12, 0, -32, 0, 0, 32, 108, 0, 56, -72, 0, 16, 0, 0, 56, -60, 0, 0, -64, 0, 0, -16, 0, 0, 44, 0, 48, 8, 0, -56, -96, 0, 0, 0, 0, -8, -16, 0, -20, 44, 0, -8, 56, 0, -96, 0, 0, 12, -8, 0, 0, -28, 0, -16, 0, 0, 0, 0, 0, 0, 96, 0, 160, 8, 0, 0, -60, 0, 8, 0, 0, 32, 60, 0, 12, 8, 0, 0, 0, 0, 80, 16, 0, 8, -40, 0, -44, 0, 0, -44, -108, 0, -92, 0, 0, -36, 0, 0, -12, 16, 0, 16, 0, 0, -24, 32, 0, 0, 56, 0, -32, 0, 0, -4, 0, 0, -48, -24, 0, 40, 12, 0, 0, 12, 0, -64, -24, 0, 0, -144, 0, 0, 12, 0, -56, 4, 0, 112, 28, 0, -48, 104, 0, 0, 0, 0, -24, 12, 0, -64, -112, 0, -176, 12, 0, 0, -72, 0, -16, 4, 0, 0, 48, 0, -16, 0, 0, 0, 0, 0, 0, 8, 0, -28, -120, 0, 0, 0, 0, -24, 0, 0, 8, 16, 0, -8, 128, 0, 0, 64, 0, -32, 84, 0, -44, 4, 0, 16, 0, 0, 140, 72, 0, 8, 0, 0, 72, 0, 0, -8, -88, 0, -12, 0, 0, 16, 84, 0, 0, -32, 0, 0, -60, 0, 64, 0, 0, 4, 0, 0, -76, -56, 0, 24, 16, 0, 28, 48, 0, 0, 112, 0, 0, 0, 0, -24, 140, 0, -32, 40, 0, 28, -128, 0, 0, 0, 0, 56, 64, 0, -32, 104, 0, 4, -96, 0, 56, 8, 0, -72, -52, 0, 0, 8, 0, 12, 0, 0, 0, 0, 0, 0, -148, 0, 40, 120, 0, 0, -24, 0, -20, 0, 0, 28, 36, 0, 0, 0, 0, 0, -40, 0, 4, -8, 0, -16, -64, 0, -8, 0, 0, 12, -24, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -4, 0, 0, 128, 44, 0, 0, -20, 0, -144, 28, 0, 4, 0, 0, -4, 36, 0, -120, 0, 0, -12, -40, 0, 16, -8, 0, 0, 24, 0, 0, -36, 0, 60, 16, 0, 16, -44, 0, -120, 4, 0, 0, 0, 0, -16, 0, 0, -8, -8, 0, -80, 0, 0, 44, 48, 0, -16, -16, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, -56, -216, 0, 0, 48, 0, 0, 0, 0, -32, -48, 0, 48, 0, 0, 0, 64, 0, 8, -140, 0, -28, -168, 0, 0, 0, 0, -104, 16, 0, 32, 0, 0, -8, 0, 0, 8, 104, 0, -96, 0, 0, 64, 28, 0, 0, 0, 0, 20, -32, 0, -4, 0, 0, 0, 84, 0, -44, -12, 0, 8, -156, 0, 24, 8, 0, 0, -32, 0, 0, 72, 0, 16, 24, 0, -32, 44, 0, -24, 0, 0, 0, 0, 0, -28, -136, 0, -40, -8, 0, 0, -60, 0, -8, -48, 0, -8, -52, 0, 0, 12, 0, 32, 0, 0, 0, 0, 0, 0, -120, 0, -64, 0, 0, 0, 196, 0, -144, 0, 0, -8, 116, 0, 0, 76, 0, 0, 216, 0, 140, 16, 0, 28, 80, 0, 104, 0, 0, 4, 36, 0, 96, 0, 0, 12, 0, 0, -128, 32, 0, -8, 0, 0, 24, 112, 0, 0, 96, 0, -72, -56, 0, 8, 0, 0, -24, 24, 0, 4, -180, 0, 72, -56, 0, -32, -48, 0, 0, -44, 0, 0, 156, 0, -44, -12, 0, 48, 64, 0, 0, -16, 0, 0, 0, 0, 20, -40, 0, 32, 160, 0, -32, -40, 0, -20, -24, 0, 64, -28, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, -48, 0, 0, -24, 0, 16, 0, 0, -36, -12, 0, 80, 0, 0, 0, -64, 0, 16, -48, 0, -24, 0, 0, 8, 0, 0, 72, 64, 0, -64, 0, 0, 0, 0, 0, 28, 88, 0, 32, 0, 0, 28, -52, 0, 0, 4, 0, -112, -60, 0, 24, 0, 0, -12, 0, 0, 96, -16, 0, 48, -88, 0, -108, 48, 0, 0, -80, 0, 0, -60, 0, 24, -148, 0, 80, -24, 0, 24, -392, 0, 0, 0, 0, -96, -40, 0, 224, 0, 0, -8, -56, 0, 104, 80, 0, -4, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -48, 0, 16, 16, 0, 0, -140, 0, -28, 0, 0, -104, 0, 0, -96, 32, 0, 0, -16, 0, 120, 0, 0, 0, 72, 0, 44, 0, 0, -24, 8, 0, 112, 0, 0, 80, 0, 0, 0, 104, 0, 20, 0, 0, -32, 0, 0, 0, -48, 0, -16, -16, 0, 32, 0, 0, 0, 8, 0, 48, 76, 0, 12, 112, 0, 48, 156, 0, 0, -64, 0, 0, 32, 0, 0, 32, 0, -4, 0, 0, -28, 4, 0, 0, 0, 0, 64, 24, 0, -44, -16, 0, 56, -8, 0, -40, -112, 0, 68, 168, 0, 0, 64, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 64, 160, 0, 0, 24, 0, 24, 0, 0, 0, -88, 0, -28, -184, 0, 0, 40, 0, 8, -16, 0, -12, -64, 0, 4, 0, 0, -128, 8, 0, -48, 0, 0, 0, 0, 0, 8, -48, 0, 8, 0, 0, 0, 84, 0, 0, 8, 0, -64, 36, 0, -32, 0, 0, -48, -140, 0, 48, 32, 0, 4, 96, 0, 84, 0, 0, 0, 168, 0, 0, 24, 0, -28, -180, 0, 0, -28, 0, 40, 0, 0, 0, 0, 0, 4, -192, 0, -96, -96, 0, 120, 100, 0, 12, -16, 0, 64, -44, 0, 0, 8, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 28, 72, 0, 0, 140, 0, -32, 0, 0, -24, 68, 0, 32, -4, 0, 0, -208, 0, 32, 0, 0, 16, -172, 0, 128, 0, 0, -56, -72, 0, 0, 0, 0, 16, 0, 0, 84, -48, 0, 40, 0, 0, 0, -60, 0, 0, 32, 0, -24, -20, 0, 32, 0, 0, -28, -80, 0, 16, 16, 0, 180, 20, 0, 0, -64, 0, 0, -16, 0, 0, -156, 0, 24, 8, 0, 88, 164, 0, -40, -72, 0, 0, 0, 0, 40, 0, 0, 56, -16, 0, 56, -104, 0, -8, -36, 0, 0, 36, 0, 0, -88, 0, -48, 0, 0, 0, 0, 0, 0, -16, 0, 24, 56, 0, 0, 16, 0, 8, 0, 0, 184, -72, 0, -12, 192, 0, 0, 168, 0, 0, -48, 0, 64, -28, 0, 32, 0, 0, 16, -80, 0, -20, 0, 0, 108, 0, 0, 76, -32, 0, -4, 0, 0, 24, 44, 0, 0, 12, 0, 112, 132, 0, 0, 0, 0, -24, 60, 0, -8, 108, 0, 64, 180, 0, 144, 88, 0, 0, -104, 0, 0, -24, 0, 32, 0, 0, -32, 8, 0, 24, 248, 0, 0, 0, 0, 0, -32, 0, -48, 48, 0, -112, 52, 0, 4, 8, 0, -16, -16, 0, 0, -168, 0, 8, 0, 0, 0, 0, 0, 0, 16, 0, -80, 0, 0, 0, 12, 0, -44, 0, 0, -8, 192, 0, 36, -144, 0, 0, 24, 0, 96, 28, 0, 36, -228, 0, -16, 0, 0, -24, 0, 0, 16, 0, 0, -40, 0, 0, 16, 16, 0, 0, 0, 0, -80, -44, 0, 0, -32, 0, -56, -128, 0, -56, 0, 0, 64, -80, 0, 0, -76, 0, -16, 0, 0, -4, 204, 0, 0, 32, 0, 0, 36, 0, 0, 0, 0, -16, 24, 0, -168, -32, 0, 0, 0, 0, 76, -208, 0, -24, 80, 0, 80, -12, 0, 0, 0, 0, -64, -136, 0, 0, 32, 0, -12, 0, 0, 0, 0, 0, 0, 16, 0, -4, -48, 0, 0, 28, 0, -32, 0, 0, -108, -4, 0, -32, -128, 0, 0, 44, 0, -72, 88, 0, 144, -56, 0, 44, 0, 0, 0, -68, 0, 8, 0, 0, -56, 0, 0, -60, 120, 0, 136, 0, 0, -48, -72, 0, 0, 136, 0, -32, 0, 0, 120, 0, 0, 16, 12, 0, 96, -112, 0, 0, 24, 0, -44, 28, 0, 0, -216, 0, 0, 4, 0, 8, -100, 0, -48, 12, 0, -20, 8, 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, 111, 7, 1, 4, 0], [1, 1, 37, 4, -1, 4, 0], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 21, "prim_orbit_index": 7, "minimal_twist": "1110.2.u.d", "char_is_minimal": true, "conrey_index": 191, "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, 0, 0, -1], [0, 1, 1, -1], [0, 0, -1, 0], [0, 1, 0, 0], [1, 1, -1, 0], [2, 0, 0, 0], [0, -1, 0, 0], [1, 2, 0, 2], [1, 0, 0, 0], [0, 0, 0, 0], [1, -1, 0, -1], [1, 0, -1, 0], [0, 0, 0, -2], [1, 0, 1, 1], [-1, 0, 0, 0], [0, 6, 0, 0], [2, 0, 2, -1], [-3, 0, 3, 0], [0, 0, 0, -1], [0, 2, 2, -2], [0, 0, 0, 0], [0, -4, 0, 0], [-1, 0, -1, -1], [0, 0, 1, 0], [0, -1, 0, -1], [0, -1, 5, 1], [0, 0, -2, 0], [0, 0, 0, -6], [0, 1, 1, -1], [-7, 0, -7, 0], [0, 0, 0, 1], [0, 0, 0, 0], [6, 0, 0, 0], [0, 2, 0, 0], [0, 2, -1, -2], [-1, 0, 6, 0], [0, 3, 0, 3], [1, 0, 1, -2], [0, 0, -1, 0], [0, 4, 0, -4], [2, 2, -2, 0], [7, 0, -7, 0], [0, 0, 0, 0], [-2, 1, 2, 0], [-4, 0, 0, 0], [0, -2, 0, -2], [0, -1, -1, 1], [-3, 0, 0, 0], [0, 1, 0, 0], [6, 0, 6, 6], [-1, 0, -1, 0], [0, 4, 0, 4], [-1, 5, 1, 0], [0, 0, 0, 0], [0, -2, 0, 0], [-3, 0, -3, 6], [0, 0, -6, 0], [0, 8, 0, 0], [1, 1, -1, 0], [-9, 0, -9, 0], [0, -7, 0, 7], [2, 4, 0, 4], [0, 0, 1, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, -6], [-4, 0, -4, -4], [2, 0, 0, 0], [0, 2, 0, 2], [2, -1, -2, 0], [0, 0, -6, 0], [0, 6, 0, 1], [-1, 1, 0, 1], [3, 0, 3, 0], [0, 0, 0, 0], [0, 1, -2, -1], [3, 0, -3, 0], [0, -1, 0, 0], [-7, 4, 0, 4], [4, 0, -4, 0], [0, 2, 0, 2], [2, -2, 0, -2], [0, 0, 6, 0], [0, -7, 0, -7], [6, 6, -6, 0], [0, 0, 0, 0], [0, 0, 0, 2], [1, 2, 0, 2], [2, 0, -2, 0], [0, 0, 0, 4], [7, -14, -7, 0], [-2, 0, -2, 0], [0, -3, 0, 3], [-1, -1, 1, 0], [7, 0, -7, 0], [0, 0, 0, 3], [0, 0, 0, 0], [1, 0, 0, 0]]}