# Stored data for newform 8036.2.a.p, downloaded from the LMFDB on 24 April 2024. {"label": "8036.2.a.p", "space_label": "8036.2.a", "level": 8036, "weight": 2, "hecke_orbit": 16, "hecke_orbit_code": 67553994444119908, "dim": 10, "is_polredabs": true, "trace_hash": 387282359046528676, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-49, -126, 253, 256, -282, -154, 110, 32, -18, -2, 1]], [5, [-192, -192, 960, 1072, -592, -614, 201, 92, -25, -4, 1]], [11, [64, 1248, 336, -3280, -1804, 1184, 705, -48, -50, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+\\beta _{2}q^{5}+(1+\\beta _{2}+\\beta _{3})q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32144, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 64.16778306430092, "hecke_ring_index": 8, "level_radical": 574, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [8036, 1, [4019, 493, 785], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 7, 41], "conrey_indexes": [1], "field_disc": 22194382796647632, "field_disc_factorization": [[2, 4], [3, 3], [51375886103351, 1]], "field_poly": [-49, -126, 253, 256, -282, -154, 110, 32, -18, -2, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.193", "prec": 17}, {"__RealLiteral__": 0, "data": "8.738", "prec": 17}, {"__RealLiteral__": 0, "data": "5.680", "prec": 17}, {"__RealLiteral__": 0, "data": "210.405", "prec": 24}, {"__RealLiteral__": 0, "data": "238.506", "prec": 24}, {"__RealLiteral__": 0, "data": "7812.955", "prec": 27}], 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