# Stored data for newform 825.6.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "825.6.a.d", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 4, "hecke_orbit_code": 13510798982775609, "dim": 2, "is_polredabs": true, "nf_label": "2.2.313.1", "trace_hash": 2100816731941489766, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-78, 1, 1]]], "qexp_display": "q-\\beta q^{2}+9q^{3}+(46+\\beta )q^{4}-9\\beta q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29700, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 132.31665134570903, "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": 2, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 313, "field_disc_factorization": [[313, 1]], "field_poly": [-78, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.915", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.265", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63.928", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [11, -1]], "trace_display": [-1, 18, 0, 18], "traces": [0, 2, -1, 18, 93, 0, -9, 18, -171, 162, 0, 242, 837, 66, 304, 0, -543, 920, -81, -2932, 0, 162, -121, -5246, -1539, 0, -16622, 1458, 524, 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