# Stored data for newform 825.6.a.u, downloaded from the LMFDB on 16 April 2024.
{"label": "825.6.a.u", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 21, "hecke_orbit_code": 90071992648074041, "dim": 10, "is_polredabs": true, "trace_hash": 1774691362065530062, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-7036608, -12856224, 7443872, 1367872, -822204, -33410, 24456, 309, -271, -1, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-9q^{3}+(22+\\beta _{2})q^{4}-9\\beta _{1}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": 10000, "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": 112046017895590711920720169818743111680585728, "field_disc_factorization": [[2, 12], [3, 1], [1433, 1], [3359, 1], [66842371, 1], [246588203, 1], [114930391777450771, 1]], "field_poly": [-7036608, -12856224, 7443872, 1367872, -822204, -33410, 24456, 309, -271, -1, 1], "hecke_ring_index_factorization": [[2, 4], [5, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "8.854", "prec": 17}, {"__RealLiteral__": 0, "data": "0.161", "prec": 17}, {"__RealLiteral__": 0, "data": "236.156", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9806.148", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": 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