# Stored data for newform 1155.2.c.a, downloaded from the LMFDB on 24 April 2024. {"label": "1155.2.c.a", "space_label": "1155.2.c", "level": 1155, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 137472509059, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 507552318210212259, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, 1]], [13, [16, 0, 1]]], "qexp_display": "q+iq^{2}+iq^{3}+q^{4}+(-2+i)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 4620, "analytic_conductor": 9.222721433457885, "hecke_ring_index": 1, "level_radical": 1155, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.519", "prec": 17}, "analytic_rank_proved": true, "char_values": [1155, 2, [386, 232, 661, 211], [2, 1, 2, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 5, 7, 11], "conrey_indexes": [694], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.001", "prec": 17}, {"__RealLiteral__": 0, "data": "2.067", "prec": 17}, {"__RealLiteral__": 0, "data": "0.206", "prec": 17}, {"__RealLiteral__": 0, "data": "17.016", "prec": 20}, {"__RealLiteral__": 0, "data": "1.751", "prec": 17}, {"__RealLiteral__": 0, "data": "173.288", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, -4, 0], "traces": [0, 2, 0, 0, 2, -4, -2, 0, 0, -2, -2, -2, 0, 0, -2, -2, -2, 0, 0, 0, -4, -2, 0, 0, -6, 6, -8, 0, 0, -8, 4, 4, 0, 0, -4, -2, -2, 0, 0, -8, -6, -20, 0, 0, -2, 4, 12, 0, 0, -2, 8, -4, 0, 0, 2, 4, -6, 0, 0, -8, -2, -4, 0, 0, -14, -8, 2, 0, 0, 12, 4, -16, 0, 0, -8, 8, 0, 0, 0, 28, 4, 2, 0, 0, -2, -4, 8, 0, 0, 24, 2, -8, 0, 0, 0, 0, -10, 0, 0, 2, 6, 12, 0, 0, -24, 4, -12, 0, 0, -28, 2, -8, 0, 0, 0, 12, -8, 0, 0, -4, 12, 2, 0, 0, 4, -4, 2, 0, 0, 8, 16, 8, 0, 0, 16, 2, -12, 0, 0, 32, -2, 0, 0, 0, 2, 16, 0, 0, 0, 40, -6, 4, 0, 0, 2, -8, -8, 0, 0, -12, -10, 12, 0, 0, -20, 2, -28, 0, 0, -6, 8, 0, 0, 0, 8, 8, 2, 0, 0, -8, 4, -36, 0, 0, 36, -8, -4, 0, 0, 2, 0, 0, 0, 0, -28, 16, -2, 0, 0, -4, 24, 16, 0, 0, -4, 40, -16, 0, 0, 0, 2, 4, 0, 0, -16, 8, 6, 0, 0, 0, 4, -16, 0, 0, -10, -6, 12, 0, 0, 44, -24, 2, 0, 0, 8, 0, -8, 0, 0, 48, 2, -4, 0, 0, -4, 4, 20, 0, 0, -28, -22, -48, 0, 0, 16, 8, -34, 0, 0, -8, -8, 8, 0, 0, 6, -12, 0, 0, 0, 64, -4, -16, 0, 0, 36, -6, 12, 0, 0, -4, 12, 8, 0, 0, -16, 0, 8, 0, 0, 26, 8, -28, 0, 0, 2, 16, -24, 0, 0, 48, 8, 8, 0, 0, 0, 8, 4, 0, 0, -16, -4, 24, 0, 0, -12, 2, 28, 0, 0, 8, 28, -16, 0, 0, 2, 32, -8, 0, 0, 0, -4, 0, 0, 0, -12, 16, 2, 0, 0, 12, -4, -4, 0, 0, 24, -24, 12, 0, 0, -20, -6, 8, 0, 0, 8, 32, 24, 0, 0, 40, 6, -38, 0, 0, -8, 0, 4, 0, 0, 20, 16, -12, 0, 0, 4, -22, 0, 0, 0, -16, 0, 16, 0, 0, -6, 2, -20, 0, 0, 68, 8, 24, 0, 0, -44, -56, 2, 0, 0, 0, -6, -60, 0, 0, 12, -4, 8, 0, 0, 20, 20, 36, 0, 0, -12, -28, -40, 0, 0, 0, 4, -12, 0, 0, -36, 16, 16, 0, 0, 8, -16, 32, 0, 0, -4, 8, -28, 0, 0, -72, 6, 2, 0, 0, -8, -48, -48, 0, 0, -68, -8, 20, 0, 0, -20, 16, 0, 0, 0, 4, 12, -60, 0, 0, 8, -4, -20, 0, 0, 16, 0, -12, 0, 0, -28, 0, -4, 0, 0, 0, 20, -32, 0, 0, 2, -28, -2, 0, 0, -8, 2, 56, 0, 0, 0, -4, -4, 0, 0, -8, -4, -12, 0, 0, 6, -24, -12, 0, 0, 48, 4, 0, 0, 0, -4, -16, 8, 0, 0, 12, 48, -56, 0, 0, 8, -6, -24, 0, 0, -26, 24, 8, 0, 0, -24, -16, 48, 0, 0, 2, 2, -36, 0, 0, -20, 56, 8, 0, 0, 4, -8, 0, 0, 0, -44, 16, 32, 0, 0, 32, 2, 4, 0, 0, 0, 12, -40, 0, 0, -48, 0, 84, 0, 0, 20, -48, 14, 0, 0, -20, 16, -28, 0, 0, 0, 8, 12, 0, 0, 0, 8, -44, 0, 0, -2, 8, 40, 0, 0, 64, -18, -28, 0, 0, 4, -4, -12, 0, 0, 8, 4, 0, 0, 0, -40, 20, 6, 0, 0, 76, -8, -12, 0, 0, 8, -14, 12, 0, 0, -16, -4, 80, 0, 0, -36, 16, -12, 0, 0, 16, -6, 20, 0, 0, 12, -16, 0, 0, 0, 8, -24, -4, 0, 0, 28, -16, 20, 0, 0, -48, 2, -84, 0, 0, -84, 0, 8, 0, 0, -48, -32, 4, 0, 0, 60, -8, -6, 0, 0, -28, 24, -20, 0, 0, 0, 36, 2, 0, 0, -48, -12, -28, 0, 0, -48, -64, 24, 0, 0, -20, 8, 16, 0, 0, 14, 0, 44, 0, 0, -52, 16, -28, 0, 0, 4, 8, -8, 0, 0, 72, -4, -16, 0, 0, -36, -24, -2, 0, 0, -2, 0, 16, 0, 0, 48, 2, 60, 0, 0, -68, -8, 0, 0, 0, -12, -80, 36, 0, 0, -16, 4, 24, 0, 0, 32, -8, 2, 0, 0, -12, 0, 76, 0, 0, 0, 4, -32, 0, 0, 36, -4, -4, 0, 0, -8, 12, -84, 0, 0, 0, 16, 16, 0, 0, 2, -12, -8, 0, 0, -24, -28, 12, 0, 0, 44, 24, -4, 0, 0, 0, 40, -24, 0, 0, 16, -24, -16, 0, 0, 72, -2, 32, 0, 0, 8, -8, 4, 0, 0, 8, 40, 80, 0, 0, -48, -8, 8, 0, 0, -108, 56, -44, 0, 0, -32, -12, 0, 0, 0, -96, 6, -26, 0, 0, 4, 12, 0, 0, 0, -40, -12, 48, 0, 0, 4, 0, -48, 0, 0, 76, 8, 20, 0, 0, 10, 12, -28, 0, 0, -28, -16, 64, 0, 0, 0, -22, 0, 0, 0, 12, -4, -104, 0, 0, -16, 8, 68, 0, 0, 16, -24, -2, 0, 0, -40, 16, -6, 0, 0, -16, -6, -24, 0, 0, 36, 72, -4, 0, 0, -12, 8, 96, 0, 0, 44, 4, 44, 0, 0, 100, -72, -40, 0, 0, 2, 32, 48, 0, 0, -32, 8, 0, 0, 0, 24, 4, 24, 0, 0, 12, 0, -12, 0, 0, 8, -4, -8, 0, 0, 0, 0, -36, 0, 0, 12, 0, 48, 0, 0, 36, 14, -54, 0, 0, -4, -20, -12, 0, 0, 0, 56, -40, 0, 0, -48, -24, 4, 0, 0, -24, 4, 28, 0, 0, 60, -44, 16, 0, 0, -48, -2, -112, 0, 0, 16, 8, -28, 0, 0, 8, -66, 8, 0, 0, -48, -32, -12, 0, 0, 28, -12, 60, 0, 0, 6, 8, 48, 0, 0, 24, 8, 84, 0, 0, -46, -60, 0, 0, 0, 2, 32, 64, 0, 0, 0, -12, -8, 0, 0, 52, 8, -48, 0, 0, 8, 0, -16, 0, 0, 24, -8, 124, 0, 0, -8, -8, 10, 0, 0, 44, -12, 84, 0, 0, 0, 16, 80, 0, 0, 100, 32, 4, 0, 0, 8, -32, 64, 0, 0, -112, -12, 0, 0, 0, -16, -4, 36, 0, 0, -2, 28, -24, 0, 0, -8, 0, 108, 0, 0, -12, -6, 48, 0, 0, -12, 32, -28, 0, 0, 24, 8, -12, 0, 0, 28, -48, -4, 0, 0, 36, 20, 0, 0, 0, 8, 4, 84, 0, 0, 4, -24, 32, 0, 0, -2, -20, 16, 0, 0, 32, 0, -8, 0, 0, 24, -88, 0, 0, 0, -32, 36, -16, 0, 0, -20, -4, 26, 0, 0, 0, 24, -8, 0, 0, -28, -20, 12, 0, 0, -12, -16, -104, 0, 0, 0, 0, 6, 0, 0, -8, 16, 128, 0, 0, -40, -28, 92, 0, 0, 80, 4, 44, 0, 0, 4, -96, 48, 0, 0, 28, -8, -132, 0, 0, 8, 8, -16, 0, 0, -16, -2, 12, 0, 0, 0, -2, 0, 0, 0, 72, 8, 8, 0, 0, 12, -6, -68, 0, 0, 72, -40, 32, 0, 0, -4, 0, -16, 0, 0, 8, -12, 0, 0, 0, 24, 56, -24, 0, 0, -68, 48, -32, 0, 0, 0, 96, -36, 0, 0, -32, 2, -112, 0, 0, -28, -12, -4, 0, 0, 0, -32, -40, 0, 0, 8, -12, 8, 0, 0, 28, 68, 4, 0, 0, -16, -4, 40, 0, 0, 8, -8, 140, 0, 0, 56, 16, -2, 0, 0, -28, 32, 80, 0, 0, -24, -16, 68, 0, 0, 4, -8, 0, 0, 0, 0, -24, 0, 0, 0, 32, -12, -68, 0, 0, 0, 48, 16, 0, 0, 68, 0, -2, 0, 0, -48, -24, -36, 0, 0, -64, 16, -40, 0, 0, 14, -128, -12, 0, 0, 0, 6, -20, 0, 0, 28, 32, 12, 0, 0, -4, 4, 76, 0, 0, -4, 8, 52, 0, 0, 42, -72, 44, 0, 0, -44, 4, 40, 0, 0, -44, -24, 4, 0, 0, 36, -44, -2, 0, 0, 48, -32, -64, 0, 0, 40, 8, -20, 0, 0, 16, -18, 24, 0, 0, 8, -16, 0, 0, 0, -100, 0, -56, 0, 0, -12, -40, 24, 0, 0, -8, 32, 8, 0, 0, -24, 0, 24, 0, 0, -68, -16, 12, 0, 0, -48, 20, 40, 0, 0, -112, 10, -8, 0, 0, -38, -52, 4, 0, 0, -12, -32, 144, 0, 0, -32, 56, 8, 0, 0, -24, 0, -48, 0, 0, 12, 12, -80, 0, 0, 48, -4, -52, 0, 0, -16, -24, 20, 0, 0, 16, 48, 72, 0, 0, -12, -2, -8, 0, 0, -44, -40, 16, 0, 0, 28, -96, 12, 0, 0, 24, -22, 0, 0, 0, 0, -16, 48, 0, 0, -12, -4, 112, 0, 0, -8, -12, -16, 0, 0, -4, 0, 6, 0, 0, 16, -12, 28, 0, 0, -32, -8, -112, 0, 0, 32, -40, 22, 0, 0, 0, 2, -96, 0, 0, -60, 32, 60, 0, 0, -28, 16, 0, 0, 0, 8, -48, 68, 0, 0, 0, 24, -48, 0, 0, 24, 12, -8, 0, 0, -16, 24, -24, 0, 0, 88, -8, -132, 0, 0, -44, -56, -8, 0, 0, -2, -36, 16, 0, 0, -20, 12, 32, 0, 0, 4, -16, 0, 0, 0, 80, -42, -84, 0, 0, -60, 32, 0, 0, 0, -92, -12, 8, 0, 0, -64, 0, -12, 0, 0, -16, -4, 44, 0, 0, 24, -88, 16, 0, 0, 36, 16, -20, 0, 0, 0, 28, 20, 0, 0, -40, 60, -8, 0, 0, 36, 0, 8, 0, 0, -56, 6, 64, 0, 0, -96, 0, -36, 0, 0, -28, -28, -4, 0, 0, -24, 8, 4, 0, 0, -44, 24, 28, 0, 0, 4, -64, 0, 0, 0, 0, -4, 118, 0, 0, -12, 60, -8, 0, 0, 84, 6, 0, 0, 0, -2, -24, -60, 0, 0, -140, 16, -2, 0, 0, 48, 8, 48, 0, 0, 60, 0, 32, 0, 0, 108, 2, 8, 0, 0, 0, -48, -72, 0, 0, 32, 36, 36, 0, 0, 0, -24, -20, 0, 0, -26, -48, -12, 0, 0, 0, 8, -108, 0, 0, 28, 40, 28, 0, 0, 12, 4, -32, 0, 0, 52, -16, -72, 0, 0, 20, 10, 0, 0, 0, 2, 44, -96, 0, 0, 16, -16, -12, 0, 0, -44, -48, 8, 0, 0, 92, -48, 144, 0, 0, -144, 4, 0, 0, 0, 68, 8, 4, 0, 0, -48, -80, -68, 0, 0, -4, -24, -68, 0, 0, 20, 76, -8, 0, 0, -16, 36, -72, 0, 0, 32, -2, -60, 0, 0, -32, 16, 0, 0, 0, 0, 0, 28, 0, 0, -16, -8, 136, 0, 0, -8, 48, 4, 0, 0, -68, -12, -24, 0, 0, -60, -40, 64, 0, 0, 54, -24, -4, 0, 0, 16, 24, 56, 0, 0, 6, -4, 116, 0, 0, -60, 36, -24, 0, 0, -24, -8, -48, 0, 0, -104, 48, 16, 0, 0, 92, 0, 0, 0, 0, -12, 32, -120, 0, 0, -68, -2, -8, 0, 0, -60, 32, -84, 0, 0, -4, 0, -132, 0, 0, 4, -32, -12, 0, 0, 168, 0, 8, 0, 0, -8, -32, 0, 0, 0, 0, 12, 24, 0, 0, -32, -8, 16, 0, 0, 40, 40, -56, 0, 0, -16, -8, -2, 0, 0, -44, -28, 56, 0, 0, -6, -136, -32, 0, 0, -100, -32, 76, 0, 0, -84, -48, -8, 0, 0, 68, 6, -48, 0, 0, 56, -8, -24, 0, 0, 8, 88, 0, 0, 0, 0, 84, 0, 0, 0, 88, -4, -40, 0, 0, -28, 44, 0, 0, 0, 16, 4, 36, 0, 0, -32, 0, -8, 0, 0, -84, 4], "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, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "1155.2.c.a", "char_is_minimal": true, "conrey_index": 694, "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], [0, 1], [0, 1], [1, 0], [-2, 1], [-1, 0], [0, 1], [0, 3], [-1, 0], [-1, -2], [-1, 0], [0, 1], [0, 4], [-1, 0], [-1, -2], [-1, 0], [0, 2], [0, -1], [0, 0], [-2, 1], [-1, 0], [0, -1], [0, -6], [-3, 0], [3, -4], [-4, 0], [0, -1], [0, 1], [-4, 0], [2, -1], [2, 0], [0, 5], [0, -1], [-2, 0], [-1, -2], [-1, 0], [0, 4], [0, 0], [-4, 0], [-3, -6], [-10, 0], [0, -1], [0, -4], [-1, 0], [2, -1], [6, 0], [0, 0], [0, -1], [-1, 0], [4, 3], [-2, 0], [0, 4], [0, 6], [1, 0], [2, -1], [-3, 0], [0, 0], [0, -4], [-4, 0], [-1, -2], [-2, 0], [0, 2], [0, -1], [-7, 0], [-4, -8], [1, 0], [0, -8], [0, 2], [6, 0], [2, -1], [-8, 0], [0, -3], [0, 0], [-4, 0], [4, 3], [0, 0], [0, -1], [0, -4], [14, 0], [2, -1], [1, 0], [0, -10], [0, 14], [-1, 0], [-2, -4], [4, 0], [0, -4], [0, -3], [12, 0], [1, 2], [-4, 0], [0, -6], [0, 2], [0, 0], [0, 0], [-5, 0], [0, 14], [0, -1], [1, 0], [3, -4]]}