# Stored data for newform 2009.2.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "2009.2.a.b", "space_label": "2009.2.a", "level": 2009, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660926937, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1835944648438884073, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, 1, 1]], [3, [1, -3, 1]]], "qexp_display": "q-\\beta q^{2}+(1+\\beta )q^{3}+(-1+\\beta )q^{4}+(1+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8036, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 16.04194576607523, "hecke_ring_index": 1, "level_radical": 287, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [2009, 1, [493, 785], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [7, 41], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "1.961", "prec": 17}, {"__RealLiteral__": 0, "data": "0.086", "prec": 17}, {"__RealLiteral__": 0, "data": "9.423", "prec": 17}, {"__RealLiteral__": 0, "data": "1.088", "prec": 17}, {"__RealLiteral__": 0, "data": "63.685", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [41, 1]], "trace_display": [-1, 3, 1, 0], "traces": [0, 2, -1, 3, -1, 1, -4, 0, 0, 1, 2, 0, 1, 6, 0, -1, -3, 6, -8, 3, -3, 0, -5, 3, 5, -7, -3, 0, 0, 9, 3, 17, 9, 5, -13, 0, 7, 2, 6, 9, -5, -2, 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