# Stored data for newform 825.6.a.m, downloaded from the LMFDB on 25 April 2024.
{"label": "825.6.a.m", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 13, "hecke_orbit_code": 54043195629110073, "dim": 7, "is_polredabs": true, "trace_hash": 356485067996307443, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-125184, -9288, 27140, 2894, -1053, -119, 9, 1]]], "qexp_display": "q+(-1-\\beta _{1})q^{2}+9q^{3}+(13+\\beta _{1}+\\beta _{2}+\\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": 20, "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": 13, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 40346548526499450613521, "field_disc_factorization": [[3, 1], [11, 1], [13, 2], [29, 1], [31, 1], [827, 1], [9730620672601, 1]], "field_poly": [92576, -51316, -13444, 5771, 358, -152, -2, 1], "hecke_ring_index_factorization": [[2, 2], [5, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.402", "prec": 17}, {"__RealLiteral__": 0, "data": "0.225", "prec": 17}, {"__RealLiteral__": 0, "data": "130.180", "prec": 24}, {"__RealLiteral__": 0, "data": "33.102", "prec": 20}, {"__RealLiteral__": 0, "data": "4309.888", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [11, -1]], "trace_display": 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