# Stored data for newform 7865.2.a.u, downloaded from the LMFDB on 26 September 2025.
{"Nk2": 31460, "analytic_conductor": 62.80234118973702, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [11, -1], [13, 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": [7865, 1, [3147, 3511, 1211], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 8, "field_disc": 455594646784, "field_disc_factorization": [[2, 8], [37, 1], [48099097, 1]], "field_poly": [5, -3, -35, -13, 34, 9, -11, -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, [5, -3, -35, -13, 34, 9, -11, -1, 1]], [3, [-1, -7, 51, 51, -26, -33, -1, 5, 1]]], "hecke_orbit": 21, "hecke_orbit_code": 90071992580972217, "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": true, "label": "7865.2.a.u", "level": 7865, "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, 11, 13], "level_radical": 715, "minimal_twist": "7865.2.a.t", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(-1+\\beta _{4})q^{3}+(1+\\beta _{2})q^{4}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "7865.2.a", "trace_display": [1, -5, -8, 9], "trace_hash": 1501668395191443814, "trace_moments": [{"__RealLiteral__": 0, "data": "0.095", 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