# Stored data for newform 1575.4.a.z, downloaded from the LMFDB on 29 March 2024. {"label": "1575.4.a.z", "space_label": "1575.4.a", "level": 1575, "weight": 4, "hecke_orbit": 26, "hecke_orbit_code": 112589990751372839, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 2175449012312536977, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [14, -8, 1]], [11, [-1999, -14, 1]], [13, [593, 50, 1]]], "qexp_display": "q+(4+\\beta )q^{2}+(10+8\\beta )q^{4}+7q^{7}+(24+\\cdots)q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 25200, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 92.92800825904146, "hecke_ring_index": 1, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "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": [1575, 1, [1226, 127, 451], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.279", "prec": 17}, {"__RealLiteral__": 0, "data": "9.177", "prec": 17}, {"__RealLiteral__": 0, "data": "3.400", "prec": 17}, {"__RealLiteral__": 0, "data": "59.993", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [7, -1]], "trace_display": [8, 0, 0, 14], "traces": [0, 2, 8, 0, 20, 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