# Stored data for newform 1176.4.a.be, downloaded from the LMFDB on 25 April 2024.
{"label": "1176.4.a.be", "space_label": "1176.4.a", "level": 1176, "weight": 4, "hecke_orbit": 31, "hecke_orbit_code": 135107988888224920, "dim": 4, "is_polredabs": true, "nf_label": "4.4.391168.1", "trace_hash": 1274671053412117567, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [22148, 1456, -300, -8, 1]], [11, [7056, 4704, -232, -40, 1]]], "qexp_display": "q+3q^{3}+(2+\\beta _{1})q^{5}+9q^{9}+(10-\\beta _{1}+\\cdots)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": 56, "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": 11, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 391168, "field_disc_factorization": [[2, 11], [191, 1]], "field_poly": [382, 0, -40, 0, 1], "hecke_ring_index_factorization": [[2, 3], [7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "3.862", "prec": 17}, {"__RealLiteral__": 0, "data": "0.270", "prec": 17}, {"__RealLiteral__": 0, "data": "41.227", "prec": 20}, {"__RealLiteral__": 0, "data": "12.969", "prec": 20}, {"__RealLiteral__": 0, "data": "685.396", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1]], "trace_display": [0, 12, 8, 0], "traces": [0, 4, 0, 12, 0, 8, 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