# Stored data for newform 648.4.a.i, downloaded from the LMFDB on 28 March 2024. {"label": "648.4.a.i", "space_label": "648.4.a", "level": 648, "weight": 4, "hecke_orbit": 9, "hecke_orbit_code": 36028797086073480, "dim": 4, "is_polredabs": true, "nf_label": "4.4.72153.1", "trace_hash": 1509726598320311974, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [1408, -503, -189, -5, 1]]], "qexp_display": "q+(1+\\beta _{2})q^{5}+(-1-\\beta _{3})q^{7}+(-4+\\cdots)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": 72, "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": 7, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 72153, "field_disc_factorization": [[3, 2], [8017, 1]], "field_poly": [12, 3, -8, -1, 1], "hecke_ring_index_factorization": [[2, 3], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.883", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "38.713", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "583.092", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1]], "trace_display": [0, 0, 5, -3], "traces": [0, 4, 0, 0, 0, 5, 0, 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