# Stored data for newform 1216.4.a.j, downloaded from the LMFDB on 19 April 2024.
{"label": "1216.4.a.j", "space_label": "1216.4.a", "level": 1216, "weight": 4, "hecke_orbit": 10, "hecke_orbit_code": 40532396713444544, "dim": 2, "is_polredabs": true, "nf_label": "2.2.177.1", "trace_hash": 1690405269235147706, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-44, 1, 1]], [5, [-152, 10, 1]]], "qexp_display": "q-\\beta q^{3}+(-6+2\\beta )q^{5}+(28+\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 19456, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 71.74632256698058, "hecke_ring_index": 1, "level_radical": 38, "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": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1216, 1, [191, 837, 705], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 19], "conrey_indexes": [1], "field_disc": 177, "field_disc_factorization": [[3, 1], [59, 1]], "field_poly": [-44, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.967", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.614", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "65.207", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [19, -1]], "trace_display": [0, -1, -10, 57], "traces": [0, 2, 0, -1, 0, -10, 0, 57, 0, 35, 0, -10, 0, -13, 0, -172, 0, -51, 0, 38, 0, -117, 0, -155, 0, 154, 0, -79, 0, 79, 0, 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