# Stored data for newform 825.4.a.c, downloaded from the LMFDB on 23 April 2024.
{"label": "825.4.a.c", "space_label": "825.4.a", "level": 825, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321850681, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 920262610140195710, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [3, 1]], [7, [7, 1]]], "qexp_display": "q-3q^{2}-3q^{3}+q^{4}+9q^{6}-7q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 13200, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 48.67657575473601, "hecke_ring_index": 1, "level_radical": 165, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 1, [551, 727, 376], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.060", "prec": 17}, {"__RealLiteral__": 0, "data": "2.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.151", "prec": 17}, {"__RealLiteral__": 0, "data": "5.052", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1], [11, -1]], "trace_display": [-3, -3, 0, -7], "traces": [0, 1, -3, -3, 1, 0, 9, -7, 21, 9, 0, 11, -3, -16, 21, 0, -71, 21, -27, 125, 0, 21, -33, -81, -63, 0, 48, -27, -7, 186, 0, -58, 45, -33, -63, 0, 9, -253, -375, 48, 0, 63, -63, 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