# Stored data for newform 1216.4.a.bd, downloaded from the LMFDB on 29 March 2024. {"label": "1216.4.a.bd", "space_label": "1216.4.a", "level": 1216, "weight": 4, "hecke_orbit": 30, "hecke_orbit_code": 130604389260854464, "dim": 5, "is_polredabs": true, "trace_hash": 1084054139834585079, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-1824, 496, 228, -47, -6, 1]], [5, [80160, 10428, -1825, -257, 5, 1]]], "qexp_display": "q+(1+\\beta _{2})q^{3}+(-1+\\beta _{2}-\\beta _{3})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 19456, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 71.74632256698058, "hecke_ring_index": 16, "level_radical": 38, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1216, 1, [191, 837, 705], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 19], "conrey_indexes": [1], "field_disc": 846464628, "field_disc_factorization": [[2, 2], [3, 1], [70538719, 1]], "field_poly": [-12, 73, -8, -28, -2, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.102", "prec": 17}, {"__RealLiteral__": 0, "data": "4.573", "prec": 17}, {"__RealLiteral__": 0, "data": "1.362", "prec": 17}, {"__RealLiteral__": 0, "data": "58.170", "prec": 20}, {"__RealLiteral__": 0, "data": "39.221", "prec": 20}, {"__RealLiteral__": 0, "data": "1139.599", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [19, 1]], "trace_display": [0, 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