# Stored data for newform 1764.4.a.ba, downloaded from the LMFDB on 19 April 2024.
{"label": "1764.4.a.ba", "space_label": "1764.4.a", "level": 1764, "weight": 4, "hecke_orbit": 27, "hecke_orbit_code": 117093590378743524, "dim": 4, "is_polredabs": true, "nf_label": "4.4.136768.1", "trace_hash": 859347523634572570, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [27748, 576, -412, 0, 1]], [11, [733072, -82944, -4136, 0, 1]], [13, [10008036, -31104, -7092, 0, 1]]], "qexp_display": "q-\\beta _{1}q^{5}+(-3\\beta _{1}+\\beta _{3})q^{11}-3\\beta _{3}q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 28224, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 104.07936925012645, "hecke_ring_index": 112, "level_radical": 42, "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": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [1764, 1, [883, 785, 1081], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 136768, "field_disc_factorization": [[2, 6], [2137, 1]], "field_poly": [119, 18, -23, -2, 1], "hecke_ring_index_factorization": [[2, 4], [7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "3.812", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "39.137", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "627.318", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1]], "trace_display": [0, 0, 0, 0], 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