# Stored data for newform 225.12.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "225.12.a.f", "space_label": "225.12.a", "level": 225, "weight": 12, "hecke_orbit": 6, "hecke_orbit_code": 22517998338179297, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 849364828392385453, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-78, 1]], [7, [-27760, 1]]], "qexp_display": "q+78q^{2}+4036q^{4}+27760q^{7}+155064q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32400, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 172.8772156259075, "hecke_ring_index": 1, "level_radical": 15, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.039", "prec": 17}, {"__RealLiteral__": 0, "data": "1.915", "prec": 17}, {"__RealLiteral__": 0, "data": "0.120", "prec": 17}, {"__RealLiteral__": 0, "data": "4.745", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "11.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1]], "trace_display": [78, 0, 0, 27760], "traces": [0, 1, 78, 0, 4036, 0, 0, 27760, 155064, 0, 0, -637836, 0, -766214, 2165280, 0, 3829264, 3084354, 0, -19511404, 0, 0, -49751208, 15312360, 0, 0, -59764692, 0, 112039360, 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