# Stored data for newform 539.8.a.a, downloaded from the LMFDB on 08 December 2025.
{"Nk2": 34496, "analytic_conductor": 168.37552873594163, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, -1], [11, -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": [539, 1, [199, 442], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 60, "field_disc_factorization": [[2, 2], [3, 1], [5, 1]], "field_poly": [-15, 0, 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, [-44, 8, 1]], [3, [-2151, -6, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 134218267, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "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": "539.8.a.a", "level": 539, "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": [7, 11], "level_radical": 77, "minimal_twist": "11.8.a.a", "nf_label": "2.2.60.1", "prim_orbit_index": 1, "qexp_display": "q+(-4+\\beta )q^{2}+(3+6\\beta )q^{3}+(-52+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "539.8.a", "trace_display": [-8, 6, 470, 0], "trace_hash": 465527381135653346, "trace_moments": [{"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "1.913", "prec": 17}, {"__RealLiteral__": 0, "data": "0.029", "prec": 17}, 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