# Stored data for newform 825.6.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "825.6.a.f", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 6, "hecke_orbit_code": 22517998237516601, "dim": 3, "is_polredabs": true, "nf_label": "3.3.307532.1", "trace_hash": 1574764003481533275, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-308, -60, 7, 1]]], "qexp_display": "q+(-2-\\beta _{1})q^{2}+9q^{3}+(24+2\\beta _{1}+\\cdots)q^{4}+\\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": 2, "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": 307532, "field_disc_factorization": [[2, 2], [76883, 1]], "field_poly": [168, -76, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.891", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.875", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "241.877", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [11, -1]], "trace_display": [-7, 27, 0, -92], "traces": [0, 3, -7, 27, 73, 0, -63, -92, -231, 243, 0, 363, 657, 90, -784, 0, -415, -1934, -567, 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