# Stored data for newform 825.6.a.i, downloaded from the LMFDB on 20 April 2024.
{"label": "825.6.a.i", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 9, "hecke_orbit_code": 36028797119628089, "dim": 3, "is_polredabs": true, "nf_label": "3.3.3368.1", "trace_hash": 1523275313911159657, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [88, -60, -2, 1]]], "qexp_display": "q+(1+\\beta _{1})q^{2}-9q^{3}+(8+4\\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": 7, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 3368, "field_disc_factorization": [[2, 3], [421, 1]], "field_poly": [11, -15, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.428", "prec": 17}, {"__RealLiteral__": 0, "data": "23.355", "prec": 20}, {"__RealLiteral__": 0, "data": "8.717", "prec": 17}, {"__RealLiteral__": 0, "data": "273.921", "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": [2, -27, 0, 232], "traces": [0, 3, 2, -27, 28, 0, -18, 232, -24, 243, 0, 363, -252, -450, -1504, 0, -1360, 334, 162, -4036, 0, -2088, 242, 7060, 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