# Stored data for newform 177.6.a.a, downloaded from the LMFDB on 20 April 2024.
{"label": "177.6.a.a", "space_label": "177.6.a", "level": 177, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663473, "dim": 11, "is_polredabs": true, "trace_hash": 2190660476924345213, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-97836992, -75608576, 22980000, 14355856, -2119008, -822892, 75693, 20480, -1135, -233, 6, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+9q^{3}+(14-\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6372, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 28.387936106897573, "hecke_ring_index": 4, "level_radical": 177, "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": [177, 1, [119, 61], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 59], "conrey_indexes": [1], "field_disc": 59061038659441797927514124532701957240684, "field_disc_factorization": [[2, 2], [37, 1], [8296373, 1], [48100666643514628790451256598371, 1]], "field_poly": [-14846072, -74443300, -23890558, 13849341, 2364885, -813818, -79077, 20782, 1067, -238, -5, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.315", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "268.680", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12919.381", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 11, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], 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