# Stored data for newform 1840.4.a.u, downloaded from the LMFDB on 18 April 2024.
{"label": "1840.4.a.u", "space_label": "1840.4.a", "level": 1840, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90071992614520624, "dim": 6, "is_polredabs": true, "trace_hash": 479134222226995795, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-3496, -1831, 1158, 215, -75, -4, 1]], [7, [-3300776, -789580, 89664, 10329, -744, -14, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{3}+5q^{5}+(2+\\beta _{1}+\\beta _{4}+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29440, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 108.56351441056273, "hecke_ring_index": 8, "level_radical": 230, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1840, 1, [1151, 1381, 737, 1201], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 5, 23], "conrey_indexes": [1], "field_disc": 23789131763885, "field_disc_factorization": [[5, 1], [109, 1], [43649783053, 1]], "field_poly": [-4032, -816, 1328, 105, -80, -2, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.304", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "82.348", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1939.447", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1], [23, 1]], "trace_display": [0, 4, 30, 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