# Stored data for newform 2009.2.a.i, downloaded from the LMFDB on 24 April 2024.
{"label": "2009.2.a.i", "space_label": "2009.2.a", "level": 2009, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36028797052520409, "dim": 3, "is_polredabs": true, "nf_label": "3.3.257.1", "trace_hash": 269549124409113201, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-3, -5, 0, 1]], [3, [7, -2, -3, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+(1+\\beta _{2})q^{3}+(1+\\beta _{1}-\\beta _{2})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": 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": "0.009", "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": 257, "field_disc_factorization": [[257, 1]], "field_poly": [3, -4, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.757", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.558", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "255.008", "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": [0, 3, 0, 0], "traces": [0, 3, 0, 3, 4, 0, -10, 0, 9, 4, 0, -8, -5, -5, 0, 0, 2, -7, -11, -13, 0, 0, 2, -1, -1, -15, -21, 6, 0, 0, 0, 2, 3, -10, 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