# Stored data for newform 1859.4.a.d, downloaded from the LMFDB on 16 April 2024.
{"label": "1859.4.a.d", "space_label": "1859.4.a", "level": 1859, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949222211, "dim": 9, "is_polredabs": true, "trace_hash": 1247756389135322901, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [2988, 9710, 2245, -7888, -345, 1144, 12, -59, 0, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1-\\beta _{3})q^{3}+(5-\\beta _{2}-\\beta _{3}+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29744, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 109.6845507006718, "hecke_ring_index": 1, "level_radical": 143, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1859, 1, [508, 1354], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [11, 13], "conrey_indexes": [1], "field_disc": 168795066425329494744921, "field_disc_factorization": [[3, 3], [61, 1], [1831, 1], [19433, 1], [2880301527241, 1]], "field_poly": [-2988, 9710, -2245, -7888, 345, 1144, -12, -59, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.783", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "172.487", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6006.735", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 9, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[11, -1], [13, 1]], "trace_display": [0, 8, -30, -25], 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