# Stored data for newform 55.2.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "55.2.a.b", "space_label": "55.2.a", "level": 55, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660924983, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 518603272395225706, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, -2, 1]]], "qexp_display": "q+(1+\\beta )q^{2}-2\\beta q^{3}+(1+2\\beta )q^{4}-q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 220, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 0.4391772111170421, "hecke_ring_index": 1, "level_radical": 55, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.026", "prec": 17}, "analytic_rank_proved": true, "char_values": [55, 1, [12, 46], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 11], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.935", "prec": 17}, {"__RealLiteral__": 0, "data": "0.139", "prec": 17}, {"__RealLiteral__": 0, "data": "9.046", "prec": 17}, {"__RealLiteral__": 0, "data": "1.990", "prec": 17}, {"__RealLiteral__": 0, "data": "59.136", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [11, -1]], "trace_display": [2, 0, -2, -4], "traces": [0, 2, 2, 0, 2, -2, -8, -4, 6, 10, -2, 2, -16, -8, -4, 0, 6, 8, 10, 0, -2, 0, 2, 0, -8, 2, 0, 0, -4, 4, 8, 0, -6, 0, 16, 4, 10, -4, 0, -16, -6, 12, 16, -12, 2, -10, -8, 0, 0, -6, 2, -16, 8, 12, -16, -2, -12, 0, -12, -8, 16, 4, 0, -20, -14, 8, -8, 8, 24, 16, 4, 0, 30, -8, -20, 0, 0, -4, 16, 8, -6, 2, 12, -12, 32, -8, -12, 32, 6, -4, -10, 16, -16, 0, 8, 0, -8, -4, -6, 10, 2, -4, -48, 8, -16, 0, 28, 4, -32, -4, -2, 32, -12, 28, 0, 0, -28, -40, 8, -16, 8, 2, -28, 0, 0, -2, -20, 20, -10, 0, 0, 0, -16, 0, 32, 0, 32, 12, 16, -8, 4, -16, 32, -8, 30, -4, 0, 0, -36, 12, -8, -24, 0, 40, -4, 0, 48, -28, 8, -32, 6, 0, 2, 16, 12, 0, -12, -12, 16, 22, -16, 0, -12, -16, 16, -4, 6, -32, -36, 8, -10, 20, 0, 64, -8, 4, 0, 8, 16, 0, 0, -16, 16, -8, 12, 16, -6, -16, 10, 32, 6, -48, 28, -8, -80, -12, 16, 0, -24, 0, -16, -32, 44, -64, 20, 12, -16, 0, -20, -16, -2, -16, 48, -16, 12, 10, 44, 28, 0, -20, 8, 0, -4, 16, 0, 0, 24, 0, -32, -24, 0, 12, 2, 0, -60, 6, -48, 0, 0, 0, -2, 24, -20, 0, 4, 16, -26, 4, 48, 8, -8, 20, -32, 12, -8, -12, 0, 64, 56, 12, 16, -8, 24, 32, -36, 2, 16, 8, -8, 0, 12, 12, -16, 20, 64, 0, 0, -24, -30, 14, 12, -32, 8, -24, 24, 8, -28, 0, -4, -16, -16, 24, -24, -64, 0, -4, 80, -44, -4, -16, 0, 32, -16, 20, -28, 20, 8, 20, -80, 4, 14, -32, 16, 0, 2, -8, 40, 32, 36, 0, 8, 8, -12, -20, -60, -8, 0, -24, -42, -32, -24, 0, 0, 40, -36, -16, -56, -12, 0, 20, -4, -32, -6, 20, 0, 0, -68, 32, 24, 24, -30, -38, 52, 0, -16, 8, 48, 0, 0, 60, 20, -24, 0, 32, 16, 0, 8, -48, 32, 56, 0, 32, 16, -40, 88, 4, 0, -60, 28, -4, -16, -16, -18, 64, -24, -8, 10, 4, 16, 0, 6, 12, -80, 0, 60, -2, 24, -4, -80, 36, -12, 96, 24, 16, -40, 12, 32, 0, 0, -40, -32, -12, -32, 0, 52, 8, -64, -8, 36, -16, 12, 0, 0, -4, 0, -32, -36, 0, 16, -32, -6, -30, -16, -48, 64, 4, -24, 32, 28, 12, 10, 12, 60, 0, 60, -16, 0, -16, 12, -32, 16, -20, 16, 16, 12, 0, -24, -24, 40, -16, -8, 0, -8, -12, -32, 0, -48, 60, -56, -72, 8, -16, 12, -32, 2, 4, 40, -32, -20, -48, 6, -24, -96, -16, 0, -10, 0, 0, 48, 8, -2, 96, 24, -12, -60, 4, -8, 128, -12, -4, 48, 16, -54, 0, -28, -8, 96, 0, 40, 80, 16, 28, -60, -4, -64, 0, -36, 0, 0, -30, -28, -40, 0, -48, 80, -4, 48, -32, 44, -6, 32, 12, 24, -64, -16, 4, -32, -68, -84, 20, 2, 0, 48, -16, 16, -32, -8, 48, 0, 48, 12, -16, 44, 12, -16, -28, 84, -4, 32, 52, 0, 24, 8, -64, -24, 0, -70, -20, 78, -16, 28, 24, -16, 12, -16, 40, -16, 24, 48, 0, -8, 16, -12, 24, -16, 16, -20, 32, 16, 0, -8, -20, 24, 40, -24, -2, -48, 20, 0, -64, 28, 16, 120, 0, -28, 0, -12, 12, -48, -40, 0, 32, 0, 8, -48, 2, -12, 0, -28, -48, 20, 0, 24, 0, -12, -20, -128, 24, -12, 0, 10, 60, -48, 48, 32, 0, 0, -8, 6, -8, 0, 0, 64, 12, 48, 0, 36, -40, -16, 24, 16, 44, -24, 0, -36, 0, -100, 32, -108, 16, -32, 4, 16, -8, -48, 0, -106, 40, -144, 8, -32, -64, 0, 24, 0, -12, 40, -64, -36, -16, -16, -56, -96, -20, 36, 8, 80, 48, 68, 80, -4, 20, 32, 0, -14, 16, 52, 8, 32, 4, -32, 40, -44, 0, 96, 8, 40, 64, -8, 48, -30, -16, -38, 0, 84, 4, -8, -56, 32, -86, 0, -48, 32, 16, -24, 0, -8, 8, 60, -8, 36, 0, -56, -20, 0, -12, 88, -60, 24, -8, 8, -32, 0, 0, 32, 24, 64, 4, 72, 16, 0, -60, -48, 8, 48, -40, 0, 64, 96, -4, 4, 64, 8, -4, -60, 0, 4, -64, 60, 0, -48, 0, -48, 64, -18, 28, 64, 4, -32, 96, -8, -56, 30, -80, -28, 32, 0, 20, 0, 16, -6, -20, -20, -8, -112, 0, 0, -64, 20, 12, -2, 40, 56, -64, -20, -16, -48, 0, -12, 80, -12, -60, 48, 56, 32, 0, -16, -12, -80, 36, 12, -16, 40, -24, 32, 12, 0, 0, -56, 64, -16, 14, -12, -64, -32, -22, 40, -4, 36, -128, 16, 32, -64, -48, 56, 0, 28, -24, 16, -8, 12, 0, -32, -24, -16, 16, -20, -128, 0, 8, -16, 16, -28, -20, 0, 4, 48, -48, -32, -16, -6, -60, -30, 80, -16, 32, -56, 20, 112, -40, 36, 2, -32, 0, -16, -8, 20, -64, 76, 0, 10, 80, 12, 0, 100, -20, 96, -72, 92, -20, 0, 48, 0, -12, 8, -64, 44, 0, -96, -64, 8, -32, 44, 64, 32, -4, -24, 40, -28, -12, 0, 0, -64, 64, -32, -8, -80, 48, -64, 64, -16, -36, 112, 0, -24, 0, -12, 88, -64, 48, 0, 64, -64, 112, 140, 16, -88, 32, -72, -24, -16, -62, 32, 20, 12, 8, -32, 4, 6, 0, -12, -40, 80, 16, -56, -16, 12, 76, -112, -4, 6, -20, 8, -72, -48, 16, -64, 32, 0, 0, -10, -48, 0, 64, -64, -32, 96, -32, 24, 64, -6], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "55.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [1, 1], [0, -2], [1, 2], [-1, 0], [-4, -2], [-2, 0], [3, 1], [5, 0], [-1, -1], [1, 0], [-8, -2], [-4, 2], [-2, -2], [0, 2], [3, 0], [4, 2], [5, 5], [0, 0], [-1, -2], [0, 4], [1, 1], [0, -2], [-4, -6], [1, 0], [0, -2], [0, -4], [-2, -4], [2, -4], [4, 2], [0, 0], [-3, 1], [0, -2], [8, 6], [2, 0], [5, 10], [-2, -4], [0, 0], [-8, 8], [-3, -1], [6, 0], [8, 4], [-6, 0], [1, 2], [-5, 0], [-4, -2], [0, 2], [0, -6], [-3, 0], [1, 1], [-8, -8], [4, -6], [6, 4], [-8, -4], [-1, 0], [-6, -2], [0, 0], [-6, -2], [-4, 4], [8, 2], [2, -8], [0, 0], [-10, 0], [-7, -2], [4, -2], [-4, -2], [4, 6], [12, 10], [8, 0], [2, 2], [0, 8], [15, 5], [-4, 2], [-10, -6], [0, -2], [0, 0], [-2, 0], [8, 0], [4, 0], [-3, 0], [1, 0], [6, 6], [-6, 0], [16, 4], [-4, -2], [-6, -6], [16, -4], [3, 1], [-2, -8], [-5, -5], [8, -4], [-8, -2], [0, 0], [4, 2], [0, 0], [-4, 6], [-2, 4], [-3, -3], [5, 0], [1, 2]]}