# Stored data for newform 8037.2.a.o, downloaded from the LMFDB on 24 April 2024.
{"label": "8037.2.a.o", "space_label": "8037.2.a", "level": 8037, "weight": 2, "hecke_orbit": 15, "hecke_orbit_code": 63050394816749413, "dim": 18, "is_polredabs": true, "trace_hash": 330983855107307913, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, 179, 890, -606, -8159, 2882, 15962, -4562, -14235, 3283, 6953, -1231, -1971, 247, 322, -25, -28, 1, 1]], [5, [24064, -89088, -452800, -232672, 648288, 545160, -362661, -409912, 88150, 154097, -3827, -31997, -2465, 3677, 507, -216, -38, 5, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}-\\beta _{10}q^{5}+(\\beta _{14}+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32148, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 64.17576810450305, "hecke_ring_index": 1, "level_radical": 2679, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [8037, 1, [4466, 1693, 7525], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [3, 19, 47], "conrey_indexes": [1], "field_disc": 317297686203364284084949302493832000, "field_disc_factorization": [[2, 6], [5, 3], [31, 1], [1279426154045823726148989122959, 1]], "field_poly": [9, -179, 890, 606, -8159, -2882, 15962, 4562, -14235, -3283, 6953, 1231, -1971, -247, 322, 25, -28, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.232", "prec": 17}, {"__RealLiteral__": 0, "data": "14.133", "prec": 20}, {"__RealLiteral__": 0, "data": "6.668", "prec": 17}, {"__RealLiteral__": 0, "data": "594.601", "prec": 24}, {"__RealLiteral__": 0, "data": "295.910", "prec": 24}, {"__RealLiteral__": 0, "data": "41436.641", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 18, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [19, 1], [47, 1]], "trace_display": [-1, 0, -5, 3], "traces": [0, 18, -1, 0, 21, -5, 0, 3, -6, 0, 7, -6, 0, 21, 9, 0, 23, 4, 0, -18, -9, 0, 28, -9, 0, 11, 1, 0, 7, -12, 0, 26, 7, 0, 26, -9, 0, 8, 1, 0, 16, -12, 0, 28, -2, 0, -33, -18, 0, 17, 29, 0, 30, -5, 0, 28, 77, 0, -6, -30, 0, -16, -16, 0, 28, 22, 0, 45, 96, 0, -2, 1, 0, -24, 19, 0, -21, -2, 0, 33, 25, 0, 18, 13, 0, -7, -3, 0, 27, 6, 0, 42, 11, 0, 1, 5, 0, 44, -58, 0, 24, 15, 0, 58, -22, 0, -20, -55, 0, 25, 32, 0, -24, -6, 0, 29, -51, 0, 30, 33, 0, -10, 7, 0, 13, 3, 0, 4, 34, 0, -42, 4, 0, -3, 10, 0, 26, 44, 0, 70, 84, 0, -14, 1, 0, 18, 27, 0, 18, 81, 0, 2, 6, 0, 77, 1, 0, 24, 21, 0, 18, 3, 0, 24, -19, 0, -51, 22, 0, 5, 13, 0, 39, -32, 0, 10, 148, 0, -31, -34, 0, 18, 106, 0, 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