# Stored data for newform 4025.2.a.z, downloaded from the LMFDB on 28 March 2024. {"label": "4025.2.a.z", "space_label": "4025.2.a", "level": 4025, "weight": 2, "hecke_orbit": 26, "hecke_orbit_code": 112589990717820857, "dim": 14, "is_polredabs": true, "trace_hash": 1636810451220468599, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-9, 133, -218, -891, 539, 1853, -27, -1330, -244, 414, 111, -58, -18, 3, 1]], [3, [7, 923, -182, -4982, -950, 6420, 1350, -3338, -712, 815, 182, -93, -22, 4, 1]], [11, [4800, -55520, 246496, -522000, 505664, -92976, -189963, 113578, -380, -12318, 1609, 443, -78, -5, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+\\beta _{7}q^{3}+(1+\\beta _{2})q^{4}+(-1+\\cdots)q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16100, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 32.13978681356535, "hecke_ring_index": 5, "level_radical": 805, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [4025, 1, [2577, 1151, 3501], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [5, 7, 23], "conrey_indexes": [1], "field_disc": 900749918024836042431115409, "field_disc_factorization": [[19, 1], [16901, 1], [2805034638326713904911, 1]], "field_poly": [-9, -133, -218, 891, 539, -1853, -27, 1330, -244, -414, 111, 58, -18, -3, 1], "hecke_ring_index_factorization": [[5, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.684", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "403.465", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21977.564", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 14, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [7, 1], [23, 1]], "trace_display": [-3, -4, 0, -14], "traces": [0, 14, -3, -4, 17, 0, -4, -14, -3, 18, 0, 5, -17, -11, 3, 0, 23, -3, -15, -2, 0, 4, -23, -14, -12, 0, -9, -25, -17, 7, 0, -3, -24, -6, -14, 0, 13, -22, -20, -10, 0, -17, 4, -18, 28, 0, 3, -30, -8, 14, 0, 4, -8, -11, 20, 0, 3, -18, -38, -22, 0, -8, 22, -18, 29, 0, -9, -39, -1, 4, 0, -5, 24, -18, 35, 0, -41, -5, 22, 10, 0, 2, 8, -24, 17, 0, -26, -5, -58, 25, 0, 11, -17, -47, -2, 0, -117, -43, -3, 55, 0, -31, 47, -87, 23, 0, -1, 23, -116, 26, 0, -8, -23, 29, 67, 0, -25, -32, -29, 3, 0, 27, 39, -31, 10, 0, 15, -55, -86, 7, 0, -26, -16, 2, 37, 0, -92, 25, 4, -41, 0, -10, 40, -62, 90, 0, -117, -4, -69, 33, 0, 23, -61, -50, 23, 0, -91, -7, -18, 4, 0, 14, 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