# Stored data for newform 1936.4.a.w, downloaded from the LMFDB on 25 April 2024.
{"label": "1936.4.a.w", "space_label": "1936.4.a", "level": 1936, "weight": 4, "hecke_orbit": 23, "hecke_orbit_code": 99079191869261712, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1939582175486781182, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-47, -2, 1]], [5, [-191, -2, 1]], [7, [52, -20, 1]]], "qexp_display": "q+(1+\\beta )q^{3}+(1+2\\beta )q^{5}+(10-\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 30976, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 114.22769777111382, "hecke_ring_index": 4, "level_radical": 22, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1936, 1, [1695, 485, 849], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 11], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.045", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.186", "prec": 17}, {"__RealLiteral__": 0, "data": "9.324", "prec": 17}, {"__RealLiteral__": 0, "data": "1.328", "prec": 17}, {"__RealLiteral__": 0, "data": "64.683", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [11, -1]], "trace_display": [0, 2, 2, 20], "traces": [0, 2, 0, 2, 0, 2, 0, 20, 0, 44, 0, 0, 0, -80, 0, 194, 0, 124, 0, 72, 0, -76, 0, 98, 0, 136, 0, 182, 0, 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