# Stored data for newform 648.4.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "648.4.a.e", "space_label": "648.4.a", "level": 648, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576591496, "dim": 2, "is_polredabs": true, "nf_label": "2.2.129.1", "trace_hash": 2287520132469252505, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [-125, -4, 1]]], "qexp_display": "q+(2+\\beta )q^{5}+(-3-\\beta )q^{7}+(5+3\\beta )q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 10368, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 38.23323768371992, "hecke_ring_index": 2, "level_radical": 6, "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": [648, 1, [487, 325, 569], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 129, "field_disc_factorization": [[3, 1], [43, 1]], "field_poly": [-32, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.928", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.255", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63.972", "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], [3, 1]], "trace_display": [0, 0, 4, -6], "traces": [0, 2, 0, 0, 0, 4, 0, -6, 0, 0, 0, 10, 0, -40, 0, 0, 0, -34, 0, 34, 0, 0, 0, -98, 0, 16, 0, 0, 0, -120, 0, -200, 0, 0, 0, -270, 0, 480, 0, 0, 0, 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