# Stored data for newform 8405.2.a.f, downloaded from the LMFDB on 13 July 2026.
{"Nk2": 33620, "analytic_conductor": 67.11426289888617, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, -1], [41, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [8405, 1, [1682, 6], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-3, 1, 1]], [3, [-3, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998170415317, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "8405.2.a.f", "level": 8405, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 41], "level_radical": 205, "minimal_twist": "205.2.a.d", "nf_label": "2.2.13.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta q^{2}+3q^{3}+(1+\\beta )q^{4}+q^{5}-3\\beta q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "8405.2.a", "trace_display": [-1, 6, 2, 3], "trace_hash": 222108923535862722, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, 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