# Stored data for newform 531.8.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "531.8.a.e", "space_label": "531.8.a", "level": 531, "weight": 8, "hecke_orbit": 5, "hecke_orbit_code": 18014398643700243, "dim": 18, "is_polredabs": true, "trace_hash": 931558462805086807, "analytic_rank": 1, "is_twist_minimal": false, "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}+(75+\\beta _{1}+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 33984, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 165.87644853206865, "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": [531, 1, [119, 415], [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], "hecke_ring_index_factorization": [[2, 12], [3, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.384", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "503.242", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "30038.507", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 18, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [59, 1]], "trace_display": [-24, 0, -678, 3081], "traces": [0, 18, -24, 0, 1358, -678, 0, 3081, -4107, 0, 3609, -15070, 0, 13662, -20861, 0, 60482, -71919, 0, 56231, -143053, 0, 274198, -150029, 0, 399672, -182846, 0, 434150, -591285, 0, 426733, -1205630, 0, 403548, -912879, 0, 7703, 417859, 0, 618020, -770959, 0, 793050, -2591274, 0, -4068019, -1410373, 0, 1637427, -1021549, 0, -3749190, -1037934, 0, 331974, 391748, 0, 653724, 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