# Stored data for newform 648.4.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "648.4.a.f", "space_label": "648.4.a", "level": 648, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203961992, "dim": 2, "is_polredabs": true, "nf_label": "2.2.201.1", "trace_hash": 1576092772032257253, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-185, -8, 1]]], "qexp_display": "q+(4+\\beta )q^{5}+(-15+\\beta )q^{7}+(-23+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 10368, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 38.23323768371992, "hecke_ring_index": 2, "level_radical": 6, "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": [648, 1, [487, 325, 569], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 201, "field_disc_factorization": [[3, 1], [67, 1]], "field_poly": [-50, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "1.896", "prec": 17}, {"__RealLiteral__": 0, "data": "0.336", "prec": 17}, {"__RealLiteral__": 0, "data": "8.806", "prec": 17}, {"__RealLiteral__": 0, "data": "2.449", "prec": 17}, {"__RealLiteral__": 0, "data": "55.630", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1]], "trace_display": [0, 0, 8, -30], "traces": [0, 2, 0, 0, 0, 8, 0, -30, 0, 0, 0, -46, 0, 92, 0, 0, 0, 22, 0, -86, 0, 0, 0, -58, 0, 184, 0, 0, 0, 108, 0, 136, 0, 0, 0, 282, 0, -180, 0, 0, 0, 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