# Stored data for newform 338.8.a.m, downloaded from the LMFDB on 10 December 2025.
{"Nk2": 21632, "analytic_conductor": 105.58613861363315, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [13, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [338, 1, [171], [1]], "cm_discs": [], "conrey_index": 1, "dim": 8, "field_disc": 3404630856398548915533297275136, "field_disc_factorization": [[2, 8], [3, 4], [37, 1], [3108109, 1], [1119098269, 1], [1275789013, 1]], "field_poly": [137733023376, 49433716800, -12575752488, 246003120, 30742777, -22320, -11090, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[3, [137733023376, 49433716800, -12575752488, 246003120, 30742777, -22320, -11090, 0, 1]], [5, [1997517058976160000, 141194419997184000, -1440334136623200, -1383675408000, 41817423121, -42080720, -334782, 304, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043195662664018, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 140608, "hecke_ring_index_factorization": [[2, 6], [13, 3]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "338.8.a.m", "level": 338, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 13], "level_radical": 26, "minimal_twist": "26.8.e.a", "prim_orbit_index": 1, "qexp_display": "q-8q^{2}+\\beta _{1}q^{3}+2^{6}q^{4}+(-38-\\beta _{1}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "338.8.a", "trace_display": [-64, 0, -304, -2160], "trace_hash": 2080768751149586400, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.107", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "141.632", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4716.279", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 8, -64, 0, 512, -304, 0, -2160, -4096, 4684, 2432, -2160, 0, 0, 17280, -21296, 32768, 41520, -37472, -66240, -19456, 51040, 17280, -7560, 0, 136980, 0, 66960, -138240, 346056, 170368, 346320, -262144, -496320, -332160, 283248, 299776, -142800, 529920, 0, 155648, -1525280, -408320, 285360, -138240, 254416, 60480, -1787952, 0, -2131660, -1095840, -478640, 0, 1833300, -535680, 1091472, 1105920, 1694208, -2768448, 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