# Stored data for newform 1521.2.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "1521.2.a.f", "space_label": "1521.2.a", "level": 1521, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170408433, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 170556409705346138, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, 2, 1]], [5, [-8, 0, 1]], [7, [-8, 0, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}+(1-2\\beta )q^{4}-2\\beta q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6084, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 12.145246147436746, "hecke_ring_index": 1, "level_radical": 39, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "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": "0.027", "prec": 17}, "analytic_rank_proved": true, "char_values": [1521, 1, [677, 847], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 13], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "1.886", "prec": 17}, {"__RealLiteral__": 0, "data": "0.164", "prec": 17}, {"__RealLiteral__": 0, "data": "8.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.935", "prec": 17}, {"__RealLiteral__": 0, "data": "58.983", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [13, 1]], "trace_display": [-2, 0, 0, 0], "traces": [0, 2, -2, 0, 2, 0, 0, 0, -6, 0, -8, -4, 0, 0, -8, 0, 6, -4, 0, 0, 16, 0, 4, 8, 0, 6, 0, 0, 16, -4, 0, 8, 6, 0, -12, 16, 0, 4, 8, 0, -8, 16, 0, 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