# Stored data for newform 7728.2.a.cg, downloaded from the LMFDB on 19 April 2024.
{"label": "7728.2.a.cg", "space_label": "7728.2.a", "level": 7728, "weight": 2, "hecke_orbit": 59, "hecke_orbit_code": 261208778421050928, "dim": 6, "is_polredabs": true, "trace_hash": 319975963661616237, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-32, -60, 100, 5, -24, 0, 1]], [11, [-64, 464, 100, -145, -33, 5, 1]], [13, [-3160, -660, 934, 81, -58, -2, 1]], [17, [-896, 1936, -1412, 372, -7, -10, 1]]], "qexp_display": "q-q^{3}+\\beta _{5}q^{5}+q^{7}+q^{9}+(-1-\\beta _{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": 30912, "fricke_eigenval": -1, "atkin_lehner_string": "++-+", "analytic_conductor": 61.70839068204548, "hecke_ring_index": 4, "level_radical": 966, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [7728, 1, [4831, 5797, 5153, 6625, 6721], [1, 1, 1, 1, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 1, "level_primes": [2, 3, 7, 23], "conrey_indexes": [1], "field_disc": 1686465665, "field_disc_factorization": [[5, 1], [337293133, 1]], "field_poly": [2, -17, 31, 7, -13, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "5.549", "prec": 17}, {"__RealLiteral__": 0, "data": "1.809", "prec": 17}, {"__RealLiteral__": 0, "data": "92.608", "prec": 20}, {"__RealLiteral__": 0, "data": "66.269", "prec": 20}, {"__RealLiteral__": 0, "data": "2428.973", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c1", 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