# Stored data for newform 1176.4.a.r, downloaded from the LMFDB on 25 April 2024.
{"label": "1176.4.a.r", "space_label": "1176.4.a", "level": 1176, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732408472, "dim": 2, "is_polredabs": true, "nf_label": "2.2.505.1", "trace_hash": 1724742181756277885, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-106, -9, 1]], [11, [-3150, -5, 1]]], "qexp_display": "q-3q^{3}+(5-\\beta )q^{5}+9q^{9}+(5-5\\beta )q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 18816, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 69.38624616675096, "hecke_ring_index": 1, "level_radical": 42, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1176, 1, [295, 589, 785, 1081], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 505, "field_disc_factorization": [[5, 1], [101, 1]], "field_poly": [-126, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.386", "prec": 17}, {"__RealLiteral__": 0, "data": "10.032", "prec": 20}, {"__RealLiteral__": 0, "data": "2.837", "prec": 17}, {"__RealLiteral__": 0, "data": "72.655", "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], [3, 1], [7, 1]], "trace_display": [0, -6, 9, 0], "traces": [0, 2, 0, -6, 0, 9, 0, 0, 0, 18, 0, 5, 0, -19, 0, -27, 0, -4, 0, 117, 0, 0, 0, 148, 0, 43, 0, -54, 0, 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