# Stored data for newform 13.16.a.a, downloaded from the LMFDB on 01 May 2024.
{"label": "13.16.a.a", "space_label": "13.16.a", "level": 13, "weight": 16, "hecke_orbit": 1, "hecke_orbit_code": 268435469, "dim": 7, "is_polredabs": true, "trace_hash": 948798812245657573, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-1457820061286400, 77633370378240, 1393638715392, 1317476032, -47667996, -121496, 345, 1]]], "qexp_display": "q+(-7^{2}-\\beta _{1})q^{2}+(-149+7\\beta _{1}+\\beta _{4}+\\cdots)q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3328, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 18.550155662989653, "hecke_ring_index": 11520, "level_radical": 13, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [13, 1, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [13], "conrey_indexes": [1], "field_disc": 56466776363471916224771021597400279268058871468, "field_disc_factorization": [[2, 2], [3, 1], [487, 1], [345533, 1], [46522607, 1], [601075758951364956031216401637, 1]], "field_poly": [2307108268997532, -31010911692567, -680104282298, 7133274223, 9594016, -172505, -2, 1], "hecke_ring_index_factorization": [[2, 8], [3, 2], [5, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.158", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "109.098", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3004.594", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "15.2.3.c1", 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