# Stored data for newform 7865.2.a.z, downloaded from the LMFDB on 21 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": 9, "field_disc": 44497650430864, "field_disc_factorization": [[2, 4], [167, 1], [16653312287, 1]], "field_poly": [2, 8, -14, -50, -6, 39, 7, -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, [2, 8, -14, -50, -6, 39, 7, -11, -1, 1]], [3, [-14, -104, -218, -46, 172, 79, -34, -17, 2, 1]]], "hecke_orbit": 26, "hecke_orbit_code": 112589990717824697, "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.z", "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.v", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{5}q^{3}+(1+\\beta _{2})q^{4}+q^{5}+\\cdots", "related_objects": [], "relative_dim": 9, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "7865.2.a", "trace_display": [1, -2, 9, 10], "trace_hash": 2131918144594955084, "trace_moments": [{"__RealLiteral__": 0, "data": "0.023", 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