# Stored data for newform 531.4.a.c, downloaded from the LMFDB on 23 April 2024.
{"label": "531.4.a.c", "space_label": "531.4.a", "level": 531, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321850387, "dim": 7, "is_polredabs": true, "trace_hash": 611491855583475617, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-44, -1736, 63, 484, -7, -41, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(4+\\beta _{2})q^{4}+(1-\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8496, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 31.330014213048266, "hecke_ring_index": 1, "level_radical": 177, "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": [531, 1, [119, 415], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 59], "conrey_indexes": [1], "field_disc": 3030963659122076, "field_disc_factorization": [[2, 2], [4656703, 1], [162720473, 1]], "field_poly": [-44, -1736, 63, 484, -7, -41, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.279", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "119.622", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4016.986", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [59, 1]], "trace_display": [0, 0, 2, -59], "traces": [0, 7, 0, 0, 26, 2, 0, -59, 21, 0, -71, 5, 0, -67, 65, 0, -94, 23, 0, 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