# Stored data for newform 475.4.a.f, downloaded from the LMFDB on 11 November 2025.
{"Nk2": 7600, "analytic_conductor": 28.025907252726793, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [19, 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": [475, 1, [77, 401], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 3144, "field_disc_factorization": [[2, 3], [3, 1], [131, 1]], "field_poly": [-8, -16, -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, [-38, -18, 3, 1]], [3, [-172, -64, 1, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998203961819, "hecke_ring_generator_nbound": 3, "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": "475.4.a.f", "level": 475, "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, 19], "level_radical": 95, "minimal_twist": "19.4.a.b", "nf_label": "3.3.3144.1", "prim_orbit_index": 1, "qexp_display": "q+(-1-\\beta _{1}+\\beta _{2})q^{2}+(\\beta _{1}-2\\beta _{2})q^{3}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "475.4.a", "trace_display": [-3, -1, 0, 35], "trace_hash": 2066514202043038336, "trace_moments": [{"__RealLiteral__": 0, "data": "0.075", "prec": 17}, {"__RealLiteral__": 0, "data": "2.917", "prec": 17}, {"__RealLiteral__": 0, "data": 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