# Stored data for newform 4165.2.a.q, downloaded from the LMFDB on 12 December 2025.
{"Nk2": 16660, "analytic_conductor": 33.25769244186328, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, -1], [7, -1], [17, -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": [4165, 1, [1667, 2551, 2451], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 8, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-1, 2, 1]], [3, [2, -4, 1]], [11, [14, 8, 1]], [13, [-8, 0, 1]]], "hecke_orbit": 17, "hecke_orbit_code": 72057594071486533, "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": "4165.2.a.q", "level": 4165, "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, 7, 17], "level_radical": 595, "minimal_twist": "85.2.a.b", "nf_label": "2.2.8.1", "prim_orbit_index": 1, "qexp_display": "q+(-1+\\beta )q^{2}+(2+\\beta )q^{3}+(1-2\\beta )q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "4165.2.a", "trace_display": [-2, 4, 2, 0], "trace_hash": 1943510594051414206, "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "1.934", "prec": 17}, {"__RealLiteral__": 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