# Stored data for newform 729.2.e.q, downloaded from the LMFDB on 31 March 2023. {"level_primes": [3], "is_polredabs": true, "sato_tate_group": "1.2.3.c9", "rm_discs": [], "conrey_indexes": [82, 163, 325, 406, 568, 649], "cm_discs": [], "trace_hash": 1515111659994382586, "level_radical": 3, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 5, "is_cm": false, "hecke_orbit": 17, "analytic_conductor": 5.82109430735134, "inner_twist_count": 4, "field_disc_factorization": [[2, 12], [3, 18]], "is_rm": false, "char_order": 9, "level_is_square": true, "weight_parity": 1, "label": "729.2.e.q", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "729.2.a.c", "field_poly_is_cyclotomic": true, "dim": 12, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 12, 0, 0, 6, 0, 0, -12, 0, 0, 12, 0, 0, -30, 0, 0, 18, 0, 0, 24, 0, 0, -30, 0, 0, 42, 0, 0, -12, 0, 0, 24, 0, 0, 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"q+\\zeta_{36}^{9}q^{2}+(1+\\zeta_{36}-\\zeta_{36}^{4})q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 1586874322944, "level_is_prime_power": true, "relative_dim": 2, "hecke_cutters": [[2, [9, 0, 27, 0, 9, 0, -24, 0, 18, 0, -3, 0, 1]], [5, [9, 0, 81, 0, 198, 0, -24, 0, 189, 0, -21, 0, 1]], [7, [1, -15, 60, 35, 21, 6, 1]]], "space_label": "729.2.e", "level": 729, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 27, 5, 1, 9, 0], [1, 1, 27, 6, -1, 18, 0]], "char_degree": 6, "char_conductor": 27, "char_orbit_index": 5, "hecke_ring_generator_nbound": 4, "hecke_orbit_code": 72057868949390041, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.302", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "916.564", "prec": 24}, {"__RealLiteral__": 0, "data": "1157.362", "prec": 27}, {"__RealLiteral__": 0, "data": 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