# Stored data for newform 1161.1.i.a, downloaded from the LMFDB on 25 April 2024. {"label": "1161.1.i.a", "space_label": "1161.1.i", "level": 1161, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 549772592265, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1543298946344808295, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+q^{4}-\\zeta_{6}q^{7}+\\zeta_{6}q^{13}+q^{16}-\\zeta_{6}^{2}q^{19}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 129, "char_orbit_label": "i", "char_is_real": false, "Nk2": 1161, "analytic_conductor": 0.5794144796669158, "hecke_ring_index": 1, "level_radical": 129, "projective_image": "D3", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "artin_degree": 18, "artin_image": "18.3", "field_poly_is_real_cyclotomic": false, "artin_field_label": "6.0.4043763.1", "projective_field_label": "3.1.49923.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [1161, 6, [947, 433], [3, 4]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [3, 43], "conrey_indexes": [350, 1025], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "1.825", "prec": 17}, {"__RealLiteral__": 0, "data": "1.549", "prec": 17}, {"__RealLiteral__": 0, "data": "15.564", "prec": 20}, {"__RealLiteral__": 0, "data": "41.354", "prec": 20}, {"__RealLiteral__": 0, "data": "204.996", "prec": 24}], "related_objects": ["ArtinRepresentation/2.3e3_43.6t5.1"], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 0, 0, -2], "traces": [0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 8, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 4, 0], "projective_field": [-43, 0, 0, 1], "artin_field": [43, 0, 0, -8, 0, 0, 1], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 43, 3, 1, 3, 0], [1, 1, 129, 6, -1, 6, 0]], "char_orbit_index": 9, "prim_orbit_index": 6, "embedded_related_objects": [["ArtinRepresentation/2.3e3_43.6t5.1c2"], ["ArtinRepresentation/2.3e3_43.6t5.1c1"]], "minimal_twist": "1161.1.i.a", "char_is_minimal": true, "conrey_index": 350, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "qexp": [[], [[1, 0]], [], [], [[1, 0]], [], [], [[-1, 1], [-1, 1]], [], [], [], [], [], [[1, 1]], [], [], [[1, 0]], [], [], [[-1, 2]], [], [], [], [], [], [[-1, 1]], [], [], [[-2, 1]], [], [], [[-1, 2]], [], [], [], [], [], [[1, 2], [1, 2]], [], [], [], [], [], [[1, 0]], [], [], [], [], [], [[3, 2]], [], [], [[1, 1]], [], [], [], [], [], [], [], [], [[1, 1]], [], [], [[1, 0]], [], [], [[1, 2], [1, 2]], [], [], [], [], [], [[-1, 1], [-1, 1]], [], [], [[-1, 2]], [], [], [[1, 1]], [], [], [], [], [], [], [], [], [], [], [], [[-2, 2]], [], [], [], [], [], [[-1, 0]], [], [], [[-1, 1]]]}