# Stored data for newform 800.4.a.o, downloaded from the LMFDB on 19 April 2024.
{"label": "800.4.a.o", "space_label": "800.4.a", "level": 800, "weight": 4, "hecke_orbit": 15, "hecke_orbit_code": 63050394850296608, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1026773336047539940, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-20, 0, 1]], [11, [-80, 0, 1]], [13, [-62, 1]]], "qexp_display": "q-\\beta q^{3}+7\\beta q^{7}-7q^{9}-2\\beta q^{11}+62q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 12800, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 47.20152800459249, "hecke_ring_index": 4, "level_radical": 10, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [800, 1, [351, 101, 577], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "1.913", "prec": 17}, {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "14.730", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "144.917", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, 1]], "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 124, 0, 0, 0, 92, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 80, 0, 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