# Stored data for newform 110.2.f.b, downloaded from the LMFDB on 22 December 2024.
{"Nk2": 440, "analytic_conductor": 0.8783544222340842, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 55, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 4, "char_parity": 1, "char_values": [110, 4, [67, 101], [3, 2]], "cm_discs": [], "conrey_index": 43, "dim": 4, "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 8, "has_non_self_twist": 1, "hecke_cutters": [[3, [1, -4, 8, -4, 1]], [13, [18, -6, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503943258308718, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 55, 5, 1, 4, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "110.2.f.b", "level": 110, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [2, 5, 11], "level_radical": 110, "minimal_twist": "110.2.f.b", "nf_label": "4.0.256.1", "prim_orbit_index": 5, "qexp_display": "q+\\zeta_{8}q^{2}+(1-\\zeta_{8}+\\zeta_{8}^{2})q^{3}+\\zeta_{8}^{2}q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "110.2.f", "trace_display": [0, 4, 0, 0], "trace_hash": 1483727727108981268, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "60.328", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1433.658", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.276", "prec": 17}, "traces": [0, 4, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, -4, 12, 0, 4, -4, -12, 8, -12, 0, 0, 4, -12, 4, -16, 0, 4, 0, 12, -12, -12, 0, -16, 0, 12, 0, -8, 0, 24, -8, 0, 12, -12, -12, 24, 0, 12, -4, 0, 0, 0, 12, 24, 4, 4, 12, -12, 12, 0, 8, 0, 12, -24, 0, 0, 12, -16, 12, 0, 0, 12, 8, 24, -12, -28, 0, -12, -12, 24, 0, 4, -12, -12, -12, -12, -24, 0, -4, 0, 0, 0, 12, -24, -8, 0, 0, 8, 0, 0, -12, 0, -24, 8, 0, 36, 0, 24, 4, -24, -24, -4, 0, -12, 0, 16, 0, 0, -4, 0, -4, -28, 12, -12, 0, 0, 0, 0, 0, 0, 12, 0, -8, 0, 0, 8, -12, -24, 4, -24, 24, 32, 12, 36, 0, 12, 0, -8, -8, -60, 12, 0, 0, 24, 36, 12, 0, 40, -12, 0, 4, 0, -24, 4, -24, 16, 24, 0, 12, 0, 36, 0, -12, 48, 0, 0, 0, 4, -24, 0, 8, 48, -36, -24, 16, -24, 0, 48, 12, -12, 12, 0, 4, 12, 24, -12, -8, 12, 24, 0, 0, -32, 24, -36, 36, -36, 0, -32, -12, 0, -24, 0, -24, 0, 0, -48, 0, -36, -24, 48, -12, -72, -4, -32, 0, 0, 0, 60, 12, 0, 36, -36, -12, -36, 0, -16, 0, 36, -36, 48, -4, 0, -24, 16, -12, 0, 0, -36, -12, -48, -8, 48, -24, 20, 0, -72, 4, -36, -12, 36, 0, 0, 48, 0, -8, 20, 0, 12, -16, 0, 4, 0, 12, 36, 32, -36, 8, 24, 24, 0, 0, 0, -20, 36, 0, -12, 24, 36, -8, 0, -12, -8, 24, -12, 8, -12, 0, 16, 12, -72, 4, 72, 0, 0, 12, 36, -48, -12, 12, 0, 12, 12, 12, 32, -36, 0, 0, -24, 44, 24, 0, 0, -36, 36, 0, -12, 0, 0, -12, 24, 0, 48, -12, 24, 0, 0, 0, -60, 0, 0, -24, 24, -24, 0, 0, 12, -24, -24, 0, -24, 36, 0, -4, -48, -8, 12, -12, 72, -12, 72, 0, -40, 0, -4, 0, 0, 36, -8, 12, 48, -8, 0, 24, 12, -36, 8, 0, 36, -12, 0, 0, 0, -8, 0, -4, 72, 12, 48, 8, 0, -24, 0, 0, -36, 0, -12, 16, -40, 12, 0, 16, -36, 16, -36, 24, -24, 0, -36, -24, -24, -48, -80, -8, 12, -48, 48, 0, -48, -12, 0, 12, -72, 24, 16, 20, 84, 0, -36, -24, -24, -12, 0, -4, -20, 0, -12, 0, 36, -24, -48, 12, 0, 36, -48, 0, -72, 0, -72, 0, 0, -8, -72, 12, 48, 0, -36, -12, -12, 60, -12, 32, 0, 24, 4, -12, -36, -60, 36, 0, 0, 12, 116, -4, -60, 0, 48, 36, -40, 36, -96, 12, 0, 36, -12, 0, 48, 0, 20, 12, 0, -16, 0, -12, 0, 0, 24, 12, -36, 36, 0, 0, 0, 24, -48, 0, 72, 48, 20, 0, 0, 72, 0, 0, -12, -40, 24, 0, 28, 24, 120, -36, 144, 24, 24, 12, -36, -36, 72, 16, 0, -72, 16, 0, 72, -36, 24, 0, -60, -56, -24, -4, 0, -36, 48, 0, -24, 0, -72, -24, -48, -28, -36, 4, 36, 0, -4, 0, 60, -24, 0, -12, 108, -48, 12, 0, -8, -24, 72, -12, 24, 36, 0, -36, 8, 72, 84, 0, -28, 72, 12, -36, -72, 16, -92, 0, 48, 72, -12, -8, 36, 0, 0, 8, -72, 8, -108, 0, 24, -48, 0, -16, 0, 36, 0, 48, -72, 24, -72, 0, 0, -24, 0, 24, -72, 0, 0, 0, 96, 32, 0, -36, -40, 36, 72, -24, 28, 0, 48, 40, 12, -24, -44, 12, -60, 20, -24, -68, 24, -24, 0, 8, -36, 48, 20, -48, -12, 0, -12, 24, 0, 0, 0, -4, -24, 0, 144, 0, 0, -36, -12, -28, -16, -36, -108, 0, -36, 0, -84, 0, 0, -16, -36, -12, 36, 0, -4, 20, -48, -20, -72, 12, 0, -48, 12, 0, 64, -60, -36, 12, 144, 16, 104, 48, -72, 0, 24, -12, 36, -48, -12, 0, 0, 12, 24, 12, -20, 0, -72, 4, 0, -12, 0, -24, -12, -108, 48, -72, 12, -48, 0, -24, 0, 0, -12, 0, -48, -48, 40, 36, 0, 24, 0, -24, 36, 0, 16, 0, -48, 48, 0, 12, -72, 72, 24, -36, 12, 24, -48, 24, 0, 36, -20, -12, 24, 72, 0, 0, -32, 48, 24, 24, 0, -24, 72, 0, -96, 0, 0, 4, 72, 36, -32, 12, 0, 0, 48, 0, 12, -8, 0, 36, 24, -12, 24, 0, -72, 84, 12, -12, 36, -24, 0, -24, 36, -48, 132, 36, -24, -36, -96, 0, 96, -32, 72, 0, -108, 72, 56, 24, 48, -4, 0, 36, 12, -16, -84, 0, 36, 48, 0, -12, 0, 56, -4, 24, 40, 0, -12, -32, 0, -12, 0, -12, 24, 0, -36, 36, 0, 0, 0, 12, -8, -24, 72, -36, 0, 0, 72, -24, 96, -36, 96, 0, 60, 36, -72, 24, -60, 60, 0, 24, 0, 24, 36, -4, -48, 0, -112, 36, -24, 0, 0, 24, -48, 0, 24, 0, 72, -36, -96, -4, 0, 16, -76, 0, -16, 0, 72, 4, 0, -24, -48, 32, -36, 0, -36, -12, -24, 24, 36, 0, 0, -60, 36, -8, 0, -48, -20, -60, -96, 0, -36, 12, -12, 0, 72, 24, -144, 0, -72, 12, 0, -12, 36, 24, 8, 0, -48, -12, 0, 72, 0, -36, -24, -44, -48, 48, 48, 48, 0, 8, 0, -76, 120, 0, -12, -24, 36, -36, 0, 0, -68, -36, -108, 96, -8, 0, 12, 36, -96, -8, -16, -36, -48, 24, 24, -24, -24, -24, 0, 8, -72, -16, -72, 96, -96, 0, 48, -80, -36, 0, 0, -24, 48, 0, -24, 0, 60, -36, 168, 32, 0, -12, 84, 0, 36, 0, 132, 48, 0, 44], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [1, -1, 1, 0], [0, 0, 1, 0], [0, 2, 0, 1], [0, 1, -1, 1], [0, -3, 0, 0], [0, 0, 0, 1], [0, -2, 0, -2], [-1, 0, 2, 0], [0, 1, 3, -1], [-1, 0, 1, -1], [3, 0, -3, 0], [0, 0, -3, 0], [1, 1, -2, 3], [-1, 0, 0, 0], [-3, 3, -3, 0], [2, 0, -2, 0], [-3, 0, 0, 0], [0, -1, 0, 2], [0, -3, 3, -3], [1, 0, 1, 3], [-3, -4, -3, 0], [1, -1, 0, 1], [-4, 0, 3, 0], [0, 3, 0, -3], [1, 0, -1, -1], [0, 0, 0, -3], [3, 3, 0, -3], [-3, 1, 1, -2], [-3, 3, 0, -3], [0, -1, 0, 0], [-4, 2, 2, -3], [0, -3, 3, -3], [3, 0, -6, 0], [0, 2, 0, -2], [-2, 0, 2, 3], [0, -3, 0, 0], [6, -3, 0, 3], [-2, 0, -1, 0], [0, 3, 6, 3], [3, 0, -3, 3], [-3, 0, 3, 6], [-3, 1, 0, 1], [6, 0, -2, 0], [0, -3, -4, -3], [3, 0, -3, 2], [-1, 1, -1, 0], [0, 0, 2, 0], [0, -4, 0, 3], [0, 6, -9, 6], [3, 0, 3, 0], [6, -5, 6, 0], [1, 1, 0, -1], [1, -3, 3, 6], [3, 0, 0, 0], [-3, 3, -3, 0], [3, 3, 3, 0], [0, 1, 0, 1], [2, -3, 1, 1], [0, -3, 3, -3], [3, -3, 3, 0], [-6, 0, 6, 0], [0, 0, -1, 0], [0, 9, 0, -3], [3, -4, 2, 2], [-4, 0, 4, 0], [3, 0, -3, 3], [0, -1, -2, -1], [0, 3, 0, -6], [3, 3, 0, -3], [2, 0, 2, 0], [6, 0, -6, 0], [-3, -2, 0, 2], [-7, 4, -1, -3], [0, 0, -3, 0], [-3, 0, -3, -9], [-3, 6, -3, 0], [6, -3, 0, 3], [0, -2, 0, -1], [1, -6, 0, 6], [-3, 0, 3, 6], [-3, 0, 3, -6], [-3, 3, 0, -3], [-3, -3, 6, -9], [-6, -3, 0, 3], [0, 3, 0, 0], [-1, -3, 1, 0], [0, 6, 3, 6], [0, 6, 0, -2], [0, -9, 0, 9], [3, 0, -3, -4], [-6, 9, -6, 0], [-2, 3, 0, -3], [0, -6, 0, -3], [0, -1, 1, -1], [2, 0, -2, -6], [0, 0, 0, 2], [0, 6, -4, -6], [-3, 0, -4, 0]]}