# Stored data for newform 2009.2.a.s, downloaded from the LMFDB on 20 April 2024.
{"label": "2009.2.a.s", "space_label": "2009.2.a", "level": 2009, "weight": 2, "hecke_orbit": 19, "hecke_orbit_code": 81064793326225369, "dim": 17, "is_polredabs": true, "trace_hash": 1446466637335828060, "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": "0.212", "prec": 17}, {"__RealLiteral__": 0, "data": "14.065", "prec": 20}, {"__RealLiteral__": 0, "data": "16.883", "prec": 20}, {"__RealLiteral__": 0, "data": "634.925", "prec": 24}, {"__RealLiteral__": 0, "data": "1913.226", "prec": 27}, {"__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, 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