# Stored data for newform 2009.2.a.k, downloaded from the LMFDB on 23 April 2024.
{"label": "2009.2.a.k", "space_label": "2009.2.a", "level": 2009, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45035996307261401, "dim": 3, "is_polredabs": true, "nf_label": "3.3.49.1", "trace_hash": 805434953713629594, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 3, -4, 1]], [3, [1, 6, 5, 1]]], "qexp_display": "q+(1+\\beta _{1})q^{2}+(-2+\\beta _{1})q^{3}+(1+2\\beta _{1}+\\cdots)q^{4}+\\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": 14, "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": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.089", "prec": 17}, {"__RealLiteral__": 0, "data": "3.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.549", "prec": 17}, {"__RealLiteral__": 0, "data": "24.892", "prec": 20}, {"__RealLiteral__": 0, "data": "1.613", "prec": 17}, {"__RealLiteral__": 0, "data": "308.465", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [41, 1]], "trace_display": [4, -5, -2, 0], "traces": [0, 3, 4, -5, 4, -2, -2, 0, 9, 4, 2, -4, 5, -7, 0, 8, 18, -3, -11, 11, 16, 0, -10, -13, -1, 5, -21, -8, 0, 2, 6, 0, 27, 2, 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