# Stored data for newform 448.8.a.k, downloaded from the LMFDB on 01 June 2026.
{"Nk2": 28672, "analytic_conductor": 139.94849141688655, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [7, 1]], "atkin_lehner_string": "++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [448, 1, [127, 197, 129], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 865, "field_disc_factorization": [[5, 1], [173, 1]], "field_poly": [-216, -1, 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, [1344, 94, 1]]], "hecke_orbit": 11, "hecke_orbit_code": 45035996407923136, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "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": "448.8.a.k", "level": 448, "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, 7], "level_radical": 14, "minimal_twist": "7.8.a.b", "nf_label": "2.2.865.1", "prim_orbit_index": 1, "qexp_display": "q+(-47-\\beta )q^{3}+(-165-5\\beta )q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "448.8.a", "trace_display": [0, -94, -330, -686], "trace_hash": 1128785455699652812, "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "1.990", "prec": 17}, {"__RealLiteral__": 0, "data": "0.110", "prec": 17}, {"__RealLiteral__": 0, "data": "9.721", "prec": 17}, {"__RealLiteral__": 0, "data": "1.015", "prec": 17}, {"__RealLiteral__": 0, "data": "65.343", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, 0, -94, 0, -330, 0, -686, 0, 1774, 0, -2844, 0, -2534, 0, 24160, 0, -1488, 0, -32810, 0, 32242, 0, -6576, 0, -58550, 0, -40420, 0, -20640, 0, -391836, 0, 33328, 0, 113190, 0, -367392, 0, -643832, 0, 734664, 0, 480476, 0, -1105810, 0, -1089108, 0, 235298, 0, -210324, 0, -2858844, 0, -32440, 0, 799900, 0, -160170, 0, 864646, 0, -608482, 0, -3396540, 0, 328648, 0, 267552, 0, -7500216, 0, 4301244, 0, -102650, 0, 975492, 0, -6408440, 0, 3414142, 0, -11659074, 0, -1155780, 0, -7143620, 0, 9772260, 0, 869162, 0, 16246872, 0, 1702800, 0, 10762752, 0, 6909332, 0, -12778314, 0, -3763556, 0, -8286880, 0, -23121312, 0, -2420280, 0, 40778124, 0, 16268424, 0, 877440, 0, 69467762, 0, 510384, 0, -29110454, 0, -14014868, 0, 21169500, 0, -43145448, 0, -27450592, 0, -23311674, 0, 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