# Stored data for newform 2009.2.a.r, downloaded from the LMFDB on 24 April 2024.
{"label": "2009.2.a.r", "space_label": "2009.2.a", "level": 2009, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698854873, "dim": 17, "is_polredabs": true, "trace_hash": 162508331206481134, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-464, -312, 5775, 299, -16136, 2029, 19567, -4259, -12183, 3251, 4173, -1231, -790, 247, 77, -25, -3, 1]], [3, [127, 265, -4959, -3186, 32237, 24596, -40386, -32352, 20338, 16946, -4973, -4316, 631, 572, -40, -38, 1, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{12}q^{3}+(1+\\beta _{2})q^{4}+\\beta _{13}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": 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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [2009, 1, [493, 785], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [7, 41], "conrey_indexes": [1], "field_disc": 118553475631403462625726443336438784, "field_disc_factorization": [[2, 10], [3, 3], [11, 1], [37, 1], [59, 1], [907, 1], [4337, 1], [45394939312301792449, 1]], "field_poly": [-464, -312, 5775, 299, -16136, 2029, 19567, -4259, -12183, 3251, 4173, -1231, -790, 247, 77, -25, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.238", "prec": 17}, {"__RealLiteral__": 0, "data": "14.065", "prec": 20}, {"__RealLiteral__": 0, "data": "4.535", "prec": 17}, {"__RealLiteral__": 0, "data": "634.925", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "49067.211", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 17, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [41, 1]], "trace_display": [3, -1, 1, 0], "traces": [0, 17, 3, -1, 25, 1, -2, 0, 9, 26, 2, 15, -4, 5, 0, 24, 33, -4, 10, -5, 26, 0, 16, 12, -16, 24, -31, 11, 0, 14, -33, 3, 16, -4, 24, 0, 57, 24, 0, 45, -36, -17, 0, 14, -9, 21, 44, -19, 60, 0, -4, 2, 25, 4, -68, -9, 0, -12, -1, 27, 66, 1, 23, 0, 75, 22, 16, 49, -45, -12, 0, 40, -23, 14, 33, -27, 9, 0, -12, 61, 82, 53, -3, 18, 0, -13, -4, 17, 74, -18, 20, 0, 28, -36, 5, 20, -148, -26, 0, 38, 15, 26, -9, -19, 32, 0, 44, -2, 25, 34, -30, -3, 0, -36, -58, 38, 14, 0, 30, 0, -84, 32, 12, 1, 10, -21, 0, 27, -35, 52, 2, -6, 26, 0, 3, 65, -30, 30, -125, 3, 0, -5, 24, 18, 73, -25, 89, 0, 81, 4, 48, 102, -52, -46, 0, -11, -11, 16, 23, -40, -50, 0, -14, 58, -25, 6, 67, -50, 0, 10, -141, 53, -26, 25, 157, 0, -27, 21, -82, 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