# Stored data for newform 245.4.e.k, downloaded from the LMFDB on 27 March 2023.
{"level_primes": [5, 7], "is_polredabs": true, "sato_tate_group": "3.2.3.c3", "rm_discs": [], "conrey_indexes": [116, 226], "cm_discs": [], "trace_hash": 472286147666992504, "level_radical": 35, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 3, "is_cm": false, "hecke_orbit": 11, "analytic_conductor": 14.455467951406451, "inner_twist_count": 2, "field_disc_factorization": [[2, 4], [3, 2], [11, 2]], "is_rm": false, "char_order": 3, "level_is_square": false, "weight_parity": 1, "label": "245.4.e.k", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "245.4.a.i", "field_poly_is_cyclotomic": false, "dim": 4, "trace_zratio": 0, "traces": [0, 4, -2, 10, -8, 10, -20, 0, 72, 4, 10, -66, 40, -20, 0, 100, 72, 70, 4, 140, -80, 0, -44, 16, 180, -50, 450, 580, 0, -516, -50, -20, 360, 330, 740, 0, -32, -328, 580, -50, 180, -600, 0, -232, -88, -20, 632, -30, 720, 0, 100, -350, 920, -540, -290, -660, 0, 1400, 1314, 380, -200, 1080, 2680, 0, -448, -50, -110, -468, -600, 160, 0, -2112, 72, -860, -1296, 250, -2880, 0, 4500, -158, -360, 1342, -1900, -80, 0, 700, -148, -1290, -1364, -240, 40, 0, -2592, 100, -910, -700, -1800, -3260, 0, -264, -200, -2020, 1850, -30, 1400, 0, -4200, 180, -1160, 1902, -110, -3280, 0, 4752, -2900, -80, 3144, -20, -2520, 0, 1800, 132, -240, -1500, -2720, -500, 0, -7336, 1744, -580, -2250, -240, -880, 0, -3288, 1450, 2140, 2440, -3160, -11200, 0, -300, -352, -1430, -144, -1290, 10520, 0, 6496, 268, 250, 1026, 1640, 280, 0, -200, -4600, -980, -7814, 2700, 3600, 0, -2684, 5520, -3200, -1650, -4360, -4500, 0, 8912, 1850, -280, -64, 5750, 13140, 0, -4752, -1900, 8120, -232, -80, 7880, 0, 10800, -944, 1640, 6700, 4070, 3760, 0, 5800, -306, -1120, -5024, 5590, -500, 0, 2856, -44, 8660, -900, 2340, -2120, 0, -6000, -1500, 5250, -32, -360, -5720, 0, -18628, 3120, -5280, 3700, -580, 10440, 0, 8868, 4300, 440, 8450, 6480, -5620, 0, -200, -3872, 2250, -7200, -220, 6320, 0, -5064, -4176, -900, 150, 3280, -1580, 0, -8004, 1800, 4760, 5940, 1120, -3360, 0, -19000, -9500, 2280, -200, 250, -2160, 0, 3872, 5076, 1750, 3296, 2460, -1480, 0, 9200, -516, 8120, -3116, 6820, -5400, 0, -2400, 2352, -3840, 1450, -2120, 5040, 0, 4800, -1650, -6480, 1240, 5600, -80, 0, 2892, 4550, 3750, 1408, 3500, -25300, 0, 1440, -1424, -6570, -8150, -12240, 23460, 0, 3800, -3968, -9570, -8356, -12400, -2000, 0, 17484, 10100, -5040, -5400, 740, 1140, 0, -300, 6700, -6620, 3500, -4710, 9000, 0, 31888, -12772, -10500, 4290, -1120, 1800, 0, -7800, 5368, 250, -2400, -9510, -19600, 0, -1100, 1496, -8640, 656, -12710, -4680, 0, -4160, -8856, 11880, 3000, 4620, 2320, 0, -5232, 400, 3550, -6888, -15720, -5960, 0, -2900, 10120, -11690, -6300, -5280, -31520, 0, -17136, 5152, -360, -4882, -10980, 1320, 0, -8600, 1200, 22210, -576, -600, -12960, 0, -27200, -4256, -13530, -1250, 1220, 44820, 0, 12416, -7200, -18340, 15094, -8160, 17440, 0, -3504, -232, 14440, 14838, 11250, -23520, 0, -2400, -19116, 790, 176, -9010, -20840, 0, -3600, 11526, -8220, 26500, -1920, 13420, 0, 13904, -10700, -3900, 9500, -12200, -20880, 0, 2528, -200, -10600, -28000, 11220, 5640, 0, -6588, 11514, 60, -15000, 1750, -3520, 0, -15520, 7150, 740, 7366, 10440, 22600, 0, -12900, -5064, -13440, 26300, -5560, -13640, 0, 9500, -6780, 16240, 1200, 18650, 2680, 0, 23164, 100, 18700, -12496, -5130, -41460, 0, 16400, 9292, 2860, 10150, -6480, 62480, 0, 27520, -9288, -500, -33392, 9310, 3680, 0, -9100, 4900, 5080, 4884, 39070, -7000, 0, -2160, -6998, -3080, 9000, 21000, -8640, 0, -24288, -8150, 1120, -13912, 22080, 55200, 0, 32572, 16000, 12090, -42500, -660, -1440, 0, -43600, 10422, 1000, -11250, 23960, -5660, 0, -20200, 17688, 22280, 17488, -6640, 18500, 0, 46656, 20300, 9500, 150, 320, -5060, 0, 57500, 3500, 19260, -2628, 16640, -31520, 0, 69944, -25700, -11880, 6958, -10500, 1520, 0, -85000, -40600, -900, -12648, 1160, -4640, 0, -11600, 9786, 9760, 19700, -3800, 19020, 0, -25264, 80, -2160, 550, -39180, -9440, 0, -41200, -8200, 22400, 14328, 2680, -9400, 0, 40700, 34282, 37160, 9400, 11880, 45300, 0, -43648, 33628, 14500, -20056, 22440, -3060, 0, -800, -448, -32030, 29376, 25120, 31440, 0, 55900, -28380, -6680, 100, -16570, -41360, 0, -55600, -6300, 7140, 11808, -1110, -6380, 0, 32352, -43300, -19000, 8718, 4500, 52840, 0, -1872, -15432, -660, -5300, 13750, 68000, 0, -2400, 17750, 1200, 35044, -16410, -15000, 0, -1584, -26250, 3080, 13600, 2320, -19320, 0, -3600, -1250, -11310, -14300, -10960, 15760, 0, -1292, 12468, -46570, -21044, -18340, 31200, 0, -55572, -2112, -8720, -27564, -18500, -20340, 0, -5800, 19300, 12520, 24156, 9020, -22500, 0, -12480, 37500, 22170, 1200, -10800, -3440, 0, -2316, -2200, -2600, 18568, -42250, -19040, 0, -5184, -31632, -20920, -14050, -8220, -81840, 0, 20160, 10000, -7250, -26624, -26350, -38720, 0, 21400, -11250, -38060, -14584, -2880, 24400, 0, -2200, -4176, -50100, 15800, -23320, -37200, 0, 1632, -28000, -12660, -54500, 1660, -41760, 0, -45892, 65250, 42320, -10208, -750, 48900, 0, 32800, 35858, 1760, 316, -21040, -74240, 0, -14300, 16672, -20010, 3216, -7840, -1440, 0, 132964, -23800, -29840, 6450, -29700, 2240, 0, 83668, 26300, -9340, -8400, 30370, -39140, 0, 30400, -23892, 3800, 12262, 16240, -95000, 0, 6120, -11400, -1340, 15368, -80, 37840, 0, 2500, -2654, 1080, -5400, -84450, 10260, 0, -31456, -20464, 9680, -8200, 52960, 50760, 0, -59152, 700, -55680, -19500, -16480, 56840, 0, 24600, -6544, 6730, 296, -500, -42840, 0, -44108, 23000, 23000, 40480, -6280, -74820, 0, -9800, -40600, 41090, -41088, 15580, -78140, 0, -5456, 21000, 41590, -13500, 38160, -40140, 0, 33100, 9000, 480, 47958, -10780, 23520, 0, -75000, 19200, -42520, 5398, -6710, -41760, 0, -21200, -24464, -27600, 12600, -2840, 87000, 0, -32000, -31474, 12000, 3364, -11100, -16500, 0, -11424, -2592, -59380, 21800, -6200, 178240, 0, 56000, -11250, 28160, -2900, -28340, -12720, 0, 70384, -17298, 7230, 41656, 22280, -3640, 0, -38880, -18750, -9250, 29728, -7040, 64760, 0, -2800, -3800, -29900, -63250, 57160, -640, 0, -168732, 12396, 52200, -28750, 27420, -14240, 0, -50820, 32850, -39900, 46908, -3260, 120160, 0, -122400, -13500, 36680, 58650, -11880, 35840, 0, 86608, 7400, 9500, -16900, 6240, -39680, 0, 81200, 44286, 42920, 19700, 41780, -2320, 0, -124000, -20206, 65940, 400, 71700, 134200, 0, 79552, 19700, 43710, -19240, 45960, -8080, 0, -37632, 25200, 18920, -55036, 27000, -10560, 0, 107300, 28978, 4720, 2850, -38280, -45760, 0, 16400, -71400, 60, -67560, -6900, 67000, 0, 150272, 33100, 510, -20350, 1400, -34540, 0, -47100, 9400, 48760, 22500, 59200, 27360, 0, 17864, -20820, 79720, 92300, 14500, -127720, 0, 101848, -4200, 1530, -5992, -21450, 179520, 0, -11200, -19818, 98000, -360, 18160, -50240, 0, -113720, -9240, -19500, -27950, -25220, -8960, 0, -89392, -1250, -38880, -17292, 12000, 82720, 0, 7608, 16362, -30650, -49000, 7140, -63780, 0, 208000, 6464, 220, 936, 30000, 14960, 0, 86600, 43200, -21210, -88578, -47560, -9000], "hecke_ring_index_factorization": [], "nf_label": "4.0.17424.3", "field_poly": [121, 0, 11, 0, 1], "has_non_self_twist": 1, "char_values": [245, 3, [197, 101], [3, 2]], "Nk2": 3920, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "e", "weight": 4, "trace_display": [-2, 10, 10, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+(-1+\\beta _{1}-\\beta _{2})q^{2}-5\\beta _{2}q^{3}+(-2\\beta _{1}+\\cdots)q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 17424, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [100, -20, 14, 2, 1]], [3, [25, -5, 1]]], "space_label": "245.4.e", "level": 245, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_degree": 2, "char_conductor": 7, "char_orbit_index": 5, "hecke_ring_generator_nbound": 4, "hecke_orbit_code": 45036271218721013, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.701", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1581.586", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 1, -1, 0], [0, 0, -5, 0], [0, -2, 4, -2], [5, 0, 5, 0], [-5, 0, 0, -5], [0, 0, 0, 0], [18, 0, 0, -2], [2, 0, 2, 0], [0, 5, -5, 5], [0, 4, 33, 4], [20, -10, 20, 0], [-5, 0, 0, -20], [0, 0, 0, 0], [25, 0, 0, 0], [36, 0, 36, 0], [0, -20, -35, -20], [0, 2, -2, 2], [70, -20, 70, 0], [-20, 0, 0, -10], [0, 0, 0, 0], [-11, 0, 0, 29], [8, -28, 8, 0], [0, -10, -90, -10], [0, 0, 25, 0], [225, -25, 225, 0], [145, 0, 0, 0], [0, 0, 0, 0], [-129, 0, 0, -48], [-25, 25, -25, 0], [0, -60, 10, -60], [0, 20, -180, 20], [165, 20, 165, 0], [185, 0, 0, -15], [0, 0, 0, 0], [-8, 0, 0, -4], [-164, 44, -164, 0], [0, 90, -290, 90], [0, -100, 25, -100], [90, 10, 90, 0], [-150, 0, 0, 100], [0, 0, 0, 0], [-58, 0, 0, 12], [-44, 50, -44, 0], [0, 0, 10, 0], [0, 36, -316, 36], [-15, 40, -15, 0], [180, 0, 0, 0], [0, 0, 0, 0], [25, 0, 0, 25], [-175, -100, -175, 0], [0, 90, -460, 90], [0, 120, 270, 120], [-145, 145, -145, 0], [-165, 0, 0, 20], [0, 0, 0, 0], [350, 0, 0, 100], [657, -177, 657, 0], [0, 40, -190, 40], [0, -50, 100, -50], [540, 60, 540, 0], [670, 0, 0, 70], [0, 0, 0, 0], [-112, 0, 0, -200], [-25, 100, -25, 0], [0, 145, 55, 145], [0, 96, 234, 96], [-300, 10, -300, 0], [40, 0, 0, 140], [0, 0, 0, 0], [-528, 0, 0, 64], [36, 4, 36, 0], [0, -200, 430, -200], [0, -208, 648, -208], [125, 0, 125, 0], [-720, 0, 0, -220], [0, 0, 0, 0], [1125, 0, 0, 125], [-79, 348, -79, 0], [0, 0, 180, 0], [0, 0, -671, 0], [-950, -50, -950, 0], [-20, 0, 0, 200], [0, 0, 0, 0], [175, 0, 0, -100], [-74, -46, -74, 0], [0, -240, 645, -240], [0, 138, 682, 138], [-120, -380, -120, 0], [10, 0, 0, 10], [0, 0, 0, 0], [-648, 0, 0, -128], [50, -300, 50, 0], [0, -55, 455, -55], [0, -100, 350, -100], [-900, 100, -900, 0], [-815, 0, 0, -180], [0, 0, 0, 0], [-66, 0, 0, 8], [-100, 50, -100, 0]]}