# Stored data for newform 825.6.a.j, downloaded from the LMFDB on 23 April 2024.
{"label": "825.6.a.j", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 10, "hecke_orbit_code": 40532396746998585, "dim": 3, "is_polredabs": true, "nf_label": "3.3.34253.1", "trace_hash": 1887677401693803912, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [140, -36, -7, 1]]], "qexp_display": "q+(2+\\beta _{1})q^{2}-9q^{3}+(7+4\\beta _{1}+\\beta _{2})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": 4, "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": 34253, "field_disc_factorization": [[34253, 1]], "field_poly": [48, -52, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "2.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.155", "prec": 17}, {"__RealLiteral__": 0, "data": "24.641", "prec": 20}, {"__RealLiteral__": 0, "data": "1.056", "prec": 17}, {"__RealLiteral__": 0, "data": "309.299", "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, 172], "traces": [0, 3, 7, -27, 25, 0, -63, 172, 231, 243, 0, -363, -225, 654, -728, 0, -415, 2366, 567, -2872, 0, 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