# Stored data for newform 147.8.a.c, downloaded from the LMFDB on 07 September 2025.
{"Nk2": 9408, "analytic_conductor": 45.9205987461659, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [147, 1, [50, 52], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 1065, "field_disc_factorization": [[3, 1], [5, 1], [71, 1]], "field_poly": [-266, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-246, 9, 1]], [5, [-74100, -360, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199388958867, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "147.8.a.c", "level": 147, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 7], "level_radical": 21, "minimal_twist": "21.8.a.b", "nf_label": "2.2.1065.1", "prim_orbit_index": 1, "qexp_display": "q+(-4-\\beta )q^{2}+3^{3}q^{3}+(154+9\\beta )q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "147.8.a", "trace_display": [-9, 54, 360, 0], "trace_hash": 897265373985346003, "trace_moments": [{"__RealLiteral__": 0, "data": "0.048", "prec": 17}, {"__RealLiteral__": 0, "data": "1.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.365", "prec": 17}, {"__RealLiteral__": 0, "data": "10.415", "prec": 20}, {"__RealLiteral__": 0, "data": "2.786", "prec": 17}, {"__RealLiteral__": 0, "data": "77.106", "prec": 20}], "trace_zratio": 0, "traces": [0, 2, -9, 54, 317, 360, -243, 0, -5067, 1458, 9030, -4932, 8559, -7708, 0, 9720, 20033, 28584, -6561, 63728, -38790, 0, 186204, 82260, -136809, 121550, 188046, 39366, 0, -435996, 243810, 29240, -347355, -133164, 167442, 0, 231093, -709556, -785196, -208116, -155910, 25056, 0, 496216, -2257812, 262440, 194280, 1575000, 540891, 0, 3287025, 771768, -2601958, 2057436, -177147, 2392440, 0, 1720656, 850122, 1101024, -1047330, -28996, -5537520, 0, 3569321, 1679760, 5027508, -4480784, 1865934, 2221020, 0, 54540, -3693843, -666604, 4803282, 3281850, 14586668, 0, 5077242, 2322952, -14509710, 1062882, 20942298, 7384392, 0, 11066520, -8597412, -11771892, 24139932, -1784448, 6582870, 0, 7958160, 789480, 1479360, 1502640, -9378585, -16266412, 0, -3595428, -15240325, -2098368, 4520934, -3923128, 30416778, 0, 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