# Stored data for newform 1040.4.a.ba, downloaded from the LMFDB on 18 October 2025.
{"Nk2": 16640, "analytic_conductor": 61.36198640597024, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [5, -1], [13, -1]], "atkin_lehner_string": "+--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [1040, 1, [911, 261, 417, 561], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 6, "field_disc": 47911485886452, "field_disc_factorization": [[2, 2], [3, 3], [173, 1], [1129, 1], [2271307, 1]], "field_poly": [-13948, -3158, 2324, 192, -97, -2, 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": [[3, [-3328, 1632, 4056, -36, -132, 0, 1]], [7, [-55504896, 6152448, 304416, -32360, -876, 38, 1]]], "hecke_orbit": 27, "hecke_orbit_code": 117093590378742800, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 256, "hecke_ring_index_factorization": [[2, 8]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1040.4.a.ba", "level": 1040, "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": [2, 5, 13], "level_radical": 130, "minimal_twist": "520.4.a.k", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{3}+5q^{5}+(-6-\\beta _{5})q^{7}+(17+\\cdots)q^{9}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1040.4.a", "trace_display": [0, 0, 30, -38], "trace_hash": 893012512634975774, "trace_moments": 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