# Stored data for newform 177.8.a.d, downloaded from the LMFDB on 24 April 2024.
{"label": "177.8.a.d", "space_label": "177.8.a", "level": 177, "weight": 8, "hecke_orbit": 4, "hecke_orbit_code": 13510799016329393, "dim": 18, "is_polredabs": true, "trace_hash": 1581647531130870274, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [8546066599350042624, -2986166801834541056, -693942416741339136, 291940745415092224, 17094064606518784, -10471805881131776, -48249714830848, 178756197263104, -3235536461632, -1636933261984, 47652762640, 8480054376, -296611506, -24830263, 951840, 38223, -1543, -24, 1]]], "qexp_display": "q+(1+\\beta _{1})q^{2}+3^{3}q^{3}+(75+\\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": 11328, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 55.29214951068955, "hecke_ring_index": 995328, "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": 3673208775720510808889856065984220684365540357197711554655816860500241755835569317031065437699842477461255675915391002177024, "field_disc_factorization": [[2, 9], [11, 1], [2390309, 1], [272853117623899545038395383148273489637130825503077041510956506827608506582444754378325133354097917838295269167073, 1]], "field_poly": [5164646074739714048, -3481290425710753600, 182609347488069978, 260578770749067175, -30152342836849520, -7379206238519716, 988557475638619, 102185027148481, -14600047830166, -774932111214, 115310342333, 3375594921, -518334228, -8403720, 1326765, 11087, -1798, -6, 1], 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