# Stored data for newform 588.6.i.e, downloaded from the LMFDB on 09 October 2026.
{"Nk2": 21168, "analytic_conductor": 94.3056860500326, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [588, 3, [295, 197, 493], [3, 3, 2]], "cm_discs": [], "conrey_index": 361, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[5, [1156, 34, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014948365959756, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "588.6.i.e", "level": 588, "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, 3, 7], "level_radical": 42, "minimal_twist": "84.6.a.b", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+(9-9\\zeta_{6})q^{3}-34\\zeta_{6}q^{5}-3^{4}\\zeta_{6}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "5.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "588.6.i", "trace_display": [0, 9, -34, 0], "trace_hash": 2017112537185459796, "trace_moments": [0, {"__RealLiteral__": 0, "data": "1.921", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "11.117", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "98.410", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 4}, "traces": [0, 2, 0, 9, 0, -34, 0, 0, 0, -81, 0, 332, 0, 2052, 0, -612, 0, 922, 0, 452, 0, 0, 0, 3776, 0, 1969, 0, -1458, 0, 2332, 0, -9792, 0, -2988, 0, 0, 0, -2390, 0, 9234, 0, 14460, 0, 9304, 0, -2754, 0, 24672, 0, 0, 0, -8298, 0, -1110, 0, -22576, 0, 8136, 0, 46892, 0, -9762, 0, 0, 0, -34884, 0, 26252, 0, 67968, 0, 130880, 0, -5606, 0, -17721, 0, 0, 0, 9840, 0, -6561, 0, -122216, 0, -62696, 0, 10494, 0, -62958, 0, 0, 0, 88128, 0, 15368, 0, 75676, 0, -53784, 0, -56146, 0, -26392, 0, 0, 0, -47124, 0, 221474, 0, -43020, 0, 108388, 0, 128384, 0, -83106, 0, 0, 0, 50827, 0, 65070, 0, -346392, 0, -491520, 0, 41868, 0, -150268, 0, 0, 0, 24786, 0, 401638, 0, -748184, 0, 444096, 0, 340632, 0, -39644, 0, 0, 0, 456042, 0, 8024, 0, -149364, 0, 665856, 0, 110078, 0, 9990, 0, 0, 0, 3628, 0, -101592, 0, -385648, 0, 1362766, 0, 36612, 0, 157142, 0, 0, 0, -422028, 0, 446868, 0, -1611276, 0, -175716, 0, -81260, 0, -306104, 0, 0, 0, 747912, 0, 577534, 0, -627912, 0, -1542196, 0, 557240, 0, -236268, 0, 0, 0, -245820, 0, 305856, 0, 300128, 0, -39320, 0, 588960, 0, -158168, 0, 0, 0, 50454, 0, 945972, 0, 1793696, 0, -318978, 0, 234228, 0, -1035626, 0, 0, 0, -457114, 0, 838848, 0, 177120, 0, 1352688, 0, -96670, 0, 59049, 0, 0, 0, 463752, 0, -549972, 0, -577752, 0, 2507264, 0, -282132, 0, -711846, 0, 0, 0, -94446, 0, 1873680, 0, 75480, 0, -1133244, 0, -1376602, 0, -781776, 0, 0, 0, -653708, 0, -2069318, 0, 1586304, 0, 3758228, 0, 670156, 0, -138312, 0, 0, 0, 569773, 0, 340542, 0, -3392220, 0, -3188656, 0, -242028, 0, 3874176, 0, 0, 0, 505314, 0, -331908, 0, 2189176, 0, -475056, 0, 1212488, 0, 1694362, 0, 0, 0, -333342, 0, 387112, 0, -848232, 0, 833488, 0, 2020194, 0, -1993266, 0, 0, 0, -1836140, 0, -193590, 0, -1785136, 0, -1947036, 0, 487746, 0, 3250944, 0, 0, 0, -1155456, 0, -3398100, 0, 68740, 0, -1495908, 0, -2502390, 0, -2224960, 0, 0, 0, 3028000, 0, 2271795, 0, 914886, 0, 381208, 0, -3209440, 0, -585630, 0, 0, 0, -1515046, 0, -1558764, 0, 2392632, 0, 1287032, 0, -2211840, 0, 4750816, 0, 0, 0, -376812, 0, -379574, 0, 6962944, 0, -2704824, 0, 334560, 0, -5421330, 0, 0, 0, 6206430, 0, -10046592, 0, 446148, 0, -1586960, 0, -4253974, 0, -3614742, 0, 0, 0, 2077672, 0, -3366828, 0, 1450968, 0, -12997332, 0, 1998432, 0, -1815418, 0, 0, 0, -3065688, 0, 1965240, 0, -8670628, 0, -713592, 0, -1706752, 0, 6477480, 0, 0, 0, -4326964, 0, -2140572, 0, 8208756, 0, 964420, 0, 2400360, 0, -72216, 0, 0, 0, -8521642, 0, -672138, 0, 11997140, 0, -9189664, 0, 2996352, 0, 8843300, 0, 0, 0, -990702, 0, 1544464, 0, 1779976, 0, 179820, 0, -6560624, 0, -2452140, 0, 0, 0, -1286492, 0, -7877720, 0, 65304, 0, 1275720, 0, 1075052, 0, 914328, 0, 0, 0, 4936460, 0, -1735416, 0, -453744, 0, 3817928, 0, 6132447, 0, 5374038, 0, 0, 0, -329508, 0, -897328, 0, 16382208, 0, 2828556, 0, -9614190, 0, 4964300, 0, 0, 0, 9028224, 0, -7821833, 0, -7596504, 0, 14835960, 0, -1602216, 0, -4021812, 0, 0, 0, -12044910, 0, -7250742, 0, -15060232, 0, 8473896, 0, -790722, 0, 527032, 0, 0, 0, 731340, 0, 10257490, 0, 9545904, 0, -5509872, 0, -5407772, 0, -1842596, 0, 0, 0, -5389674, 0, 8245524, 0, 13462416, 0, 14869888, 0, -1154078, 0, -5197806, 0, 0, 0, 368520, 0, -2825604, 0, 14329288, 0, -8851968, 0, -6939882, 0, 14553402, 0, 0, 0, -5015160, 0, 10431984, 0, -833716, 0, -4252824, 0, 1728118, 0, -7908336, 0, 0, 0, 25313472, 0, 11376138, 0, -4424760, 0, -17545420, 0, 14411020, 0, -2752704, 0, 0, 0, -264461, 0, 1350576, 0, -4407160, 0, -25893200, 0, -176940, 0, 8355840, 0, 0, 0, -5300640, 0, 4890350, 0, -2452072, 0, -2847024, 0, 12109848, 0, -15568144, 0, 0, 0, -9286974, 0, -5109112, 0, 908172, 0, 903224, 0, -1855082, 0, -8513748, 0, 0, 0, 4402816, 0, 8071632, 0, -6481968, 0, 42906820, 0, -1435401, 0, 15698670, 0, 0, 0, -2108052, 0, -14024964, 0, -27311384, 0, -18641268, 0, -1138860, 0, -18981868, 0, 0, 0, 12719128, 0, 6666060, 0, -8228052, 0, 44561116, 0, 1080280, 0, -7549632, 0, 0, 0, 476266, 0, 797040, 0, -73949184, 0, -23162976, 0, 6087096, 0, -263568, 0, 0, 0, 870030, 0, 2295854, 0, -18566384, 0, 1062882, 0, 4289144, 0, -18954738, 0, 0, 0, -8715664, 0, -19545396, 0, 8347536, 0, 30936576, 0, 15505428, 0, 4949748, 0, 0, 0, 14518752, 0, -2599884, 0, -545632, 0, 17089548, 0, 11282688, 0, -8503982, 0, 0, 0, 2539188, 0, 48111192, 0, 33316156, 0, -12813228, 0, 21732590, 0, 19280448, 0, 0, 0, 3267960, 0, 21726080, 0, -1700028, 0, -7485304, 0, 2056020, 0, -16863120, 0, 0, 0, -10015812, 0, 339660, 0, -63528204, 0, 45495168, 0, -5099598, 0, 1861192, 0, 0, 0, 12389418, 0, 21405046, 0, 13228648, 0, -14071968, 0, 123352, 0, 2102704, 0, 0, 0, -17800630, 0, 12381800, 0, -11766744, 0, -43455864, 0, -13589330, 0, 18623862, 0, 0, 0, 6556016, 0, 7138368, 0, 342544, 0, -38303186, 0, 16912026, 0, -23167022, 0, 0, 0, -6031404, 0, 9024640, 0, -58034476, 0, -2489616, 0, -38496654, 0, -19845844, 0, 0, 0, 17083288, 0, 5342828, 0, 10255914, 0, 6533760, 0, 26934552, 0, -3064878, 0, 0, 0, 25380962, 0, -15264990, 0, 51916044, 0, 8753320, 0, -14348952, 0, 32330952, 0, 0, 0, 2178252, 0, -11151744, 0, -30387024, 0, 69735168, 0, -11417472, 0, 1023420, 0, 0, 0, 27391692, 0, 36710772, 0, 9095652, 0, 70452240, 0, -20287856, 0, 2987172, 0, 0, 0, 3169784, 0, 9851292, 0, 134282880, 0, -9411820, 0, -2137752, 0, -29803014, 0, 0, 0, -10912392, 0, -10407536, 0, 32462444, 0, 30498516, 0, 10975910, 0, 27300480, 0, 0, 0, -3503036, 0, -5751756, 0, -6000156, 0, -20023948, 0, 25429008, 0, -3484008, 0, 0, 0, -67254113, 0, -3817044, 0, -39272312, 0, -1305968, 0, 3750696, 0, -12489684, 0, 0, 0, -18181746, 0, 7434078, 0, -41804112, 0, -35878788, 0, 24490392, 0, 26217332, 0, 0, 0, 17565952, 0, -48746384, 0, -33050520, 0, -37892320, 0, 2352422, 0, 1742310, 0], "weight": 6, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [9, -9], [0, 0], [0, -34], [0, 0], [0, 0], [0, 0], [0, -81], [0, 0], [332, -332], [0, 0], [1026, 0], [0, 0], [-306, 0], [0, 0], [922, -922], [0, 0], [0, 452], [0, 0], [0, 0], [0, 0], [0, 3776], [0, 0], [1969, -1969], [0, 0], [-729, 0], [0, 0], [1166, 0], [0, 0], [-9792, 9792], [0, 0], [0, -2988], [0, 0], [0, 0], [0, 0], [0, -2390], [0, 0], [9234, -9234], [0, 0], [7230, 0], [0, 0], [4652, 0], [0, 0], [-2754, 2754], [0, 0], [0, 24672], [0, 0], [0, 0], [0, 0], [0, -8298], [0, 0], [-1110, 1110], [0, 0], [-11288, 0], [0, 0], [4068, 0], [0, 0], [46892, -46892], [0, 0], [0, -9762], [0, 0], [0, 0], [0, 0], [0, -34884], [0, 0], [26252, -26252], [0, 0], [33984, 0], [0, 0], [65440, 0], [0, 0], [-5606, 5606], [0, 0], [0, -17721], [0, 0], [0, 0], [0, 0], [0, 9840], [0, 0], [-6561, 6561], [0, 0], [-61108, 0], [0, 0], [-31348, 0], [0, 0], [10494, -10494], [0, 0], [0, -62958], [0, 0], [0, 0], [0, 0], [0, 88128], [0, 0], [15368, -15368], [0, 0], [37838, 0], [0, 0], [-26892, 0], [0, 0]]}