# Stored data for newform 1089.2.a.k, downloaded from the LMFDB on 19 April 2024.
{"label": "1089.2.a.k", "space_label": "1089.2.a", "level": 1089, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45035996307260481, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1656643450312367974, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-2, 1]], [5, [4, 1]], [7, [-1, 1]]], "qexp_display": "q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4356, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 8.695708780117434, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [1089, 1, [848, 244], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 11], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.972", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.902", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.680", "prec": 17}], "related_objects": ["EllipticCurve/Q/1089/k"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [11, -1]], "trace_display": [2, 0, -4, 1], "traces": [0, 1, 2, 0, 2, -4, 0, 1, 0, 0, -8, 0, 0, -2, 2, 0, -4, -4, 0, -3, -8, 0, 0, -2, 0, 11, -4, 0, 2, -6, 0, -5, -8, 0, -8, -4, 0, 3, -6, 0, 0, 2, 0, 12, 0, 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