# Stored data for newform 2304.4.a.by, downloaded from the LMFDB on 19 April 2024.
{"label": "2304.4.a.by", "space_label": "2304.4.a", "level": 2304, "weight": 4, "hecke_orbit": 51, "hecke_orbit_code": 225179981435635968, "dim": 4, "is_polredabs": true, "nf_label": "4.4.9792.1", "trace_hash": 791011491810360898, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [9792, 0, -336, 0, 1]], [7, [9792, 0, -1104, 0, 1]], [11, [-368, 24, 1]], [13, [12690432, 0, -8640, 0, 1]], [17, [-3708, 60, 1]], [19, [-4464, -24, 1]]], "qexp_display": "q+\\beta _{1}q^{5}+(-\\beta _{1}+\\beta _{3})q^{7}+(-12-\\beta _{2}+\\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": 36864, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 135.94040065322636, "hecke_ring_index": 1024, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [2304, 1, [1279, 2053, 1793], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 9792, "field_disc_factorization": [[2, 6], [3, 2], [17, 1]], "field_poly": [7, 2, -7, -2, 1], "hecke_ring_index_factorization": [[2, 10]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.745", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "75.081", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2140.806", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], 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