Sharedwww / Tables / eigen_k8_N1-99_prec97.gpOpen in CoCalc
\\ This is a table of the first 97 Hecke eigenvalues
\\ of newforms for Gamma_0(N).
\\ Notation:
\\ f[N,k]  = [ 
\\            [g(x), [wq's], [a2(x),...,ap(x)]],
\\                  ...  
\\            [g(x), [wq's], [a2(x),...,ap(x)]]
\\          ];
\\ Where Q_f = Q(...a_n...) = Q[x]/g(x).
\\ The newforms are ordered by dimension, 
\\ then W_q's, then traces.

\\ William Stein ([email protected])

\\ uncomment the following two lines to make PARI-readable.
\\ {
\\ f = matrix(99,8);

f[2,8]=[
[x+8, [1], [-8,12,-210,1016,1092,1382,14706,-39940,68712,-102570,227552,160526,10842,-630748,472656,-1494018,2640660,827702,-126004,-1414728,980282,-3566800,5672892,-11951190,8682146]]];

f[3,8]=[
[x-6, [1], [6,-27,390,-64,-948,-5098,28386,-8620,-15288,36510,-276808,268526,-629718,685772,583296,-428058,1306380,300662,-507244,5560632,1369082,-6913720,-4376748,-8528310,-8826814]]];

f[5,8]=[
[x+14, [-1], [-14,-48,125,-1644,172,3862,-12254,-25940,12972,-81610,-156888,110126,467882,-499208,-396884,-1280498,-1337420,-923978,-797304,5103392,-4267478,-960,6140832,2010570,-4881934]],
[x^2-20*x+24, [1], [x,-8*x+90,-125,56*x-610,400*x-1728,-608*x+7850,-1184*x-1830,-320*x+22580,-408*x-57990,19520*x-231330,-2800*x+181412,25536*x-316870,-56800*x+700182,43192*x-220270,45496*x-507690,-53408*x-661710,-227360*x+1713540,160000*x-471478,-79384*x+3052070,-70000*x+1010892,-226208*x+4546610,-472480*x+6891320,490392*x-9800430,317760*x-164790,561696*x-3312190]]];

f[6,8]=[
[x-8, [-1,-1], [8,27,-114,-1576,7332,-3802,-6606,24860,41448,-41610,33152,-36466,-639078,-156412,-433776,786078,745140,-1660618,-3290836,5716152,2659898,3807440,2229468,5991210,-4060126]]];

f[7,8]=[
[x+6, [-1], [-6,-42,-84,343,-5568,-5152,-13986,55370,-91272,41610,150332,-136366,-510258,-172072,-519036,-59202,1979250,-2988748,2409404,1504512,-1821022,-1669240,696738,5558490,9876734]],
[x^2+3*x-214, [1], [x,-2*x+44,-10*x+150,-343,116*x+1596,882*x+2590,-324*x-1230,858*x+17692,-48*x-3360,9380*x+24390,-2508*x-199680,-27180*x+142926,23716*x+402906,5628*x-231796,-36900*x-599904,5184*x+1437198,-53622*x-348,57558*x-345986,-50928*x-240716,130872*x-3553800,-191928*x+1862730,-277080*x-3619840,132594*x+6028428,-363184*x+4341354,94668*x+5523378]]];

f[8,8]=[
[x-44, [1], [0,44,430,-1224,-3164,6118,-16270,-5476,1576,122838,251360,-52338,-319398,710788,284112,296062,-897548,-884810,4659692,-2710792,-5670854,-5124176,-1563556,11605674,10931618]],
[x+84, [-1], [0,-84,-82,-456,-2524,-10778,-11150,4124,81704,99798,-40480,-419442,141402,-690428,-682032,1813118,-966028,1887670,2965868,-2548232,-1680326,4038064,-5385764,-6473046,-6065758]]];

f[9,8]=[
[x+6, [-1], [-6,0,-390,-64,948,-5098,-28386,-8620,15288,-36510,-276808,268526,629718,685772,-583296,428058,-1306380,300662,-507244,-5560632,1369082,-6913720,4376748,8528310,-8826814]],
[x^2-360, [1], [x,0,-16*x,260,-320*x,6890,1248*x,33176,1664*x,-7280*x,1508,-380770,4640*x,7640,29824*x,54288*x,-142720*x,-988858,3857360,222720*x,-2004730,2699684,142912*x,408000*x,-12957490]]];

f[10,8]=[
[x-8, [-1,-1], [8,28,125,104,-5148,-8602,20274,45500,-72072,231510,-80128,104654,584922,-795532,425664,1500798,246420,893942,-2336836,-203688,-3805702,5053040,-45492,980010,-5247646]]];

f[11,8]=[
[x^2+8*x-44, [-1], [x,-6*x-27,20*x-155,82*x-286,1331,518*x+2244,-3666*x-18898,-2982*x-29568,4290*x-13583,-11468*x+43648,20210*x+52257,-3748*x-453841,68870*x+133672,12760*x+188782,-15252*x+770248,66388*x+1073794,-147078*x-1815377,-28900*x-3125188,-392590*x-1657709,452890*x+1235827,-195234*x-337964,323896*x+3196314,-175068*x-1841730,201740*x-5934025,174936*x+665705]],
[x^4-558*x^2+140*x+51744, [1], [x,-1/252*x^3-5/18*x^2+349/126*x+205/3,3/28*x^3-1/2*x^2-543/14*x+285,-1/14*x^3-5*x^2-15/7*x+1430,-1331,5/2*x^3+15*x^2-1205*x-2860,23/7*x^3+70*x^2-5834/7*x-5610,-65/7*x^3-90*x^2+20310/7*x+41096,-421/28*x^3-105/2*x^2+122289/14*x+10815,-615/14*x^3+637*x^2+122795/7*x-123816,-445/28*x^3-577/2*x^2+135145/14*x+126287,-3075/28*x^3+705/2*x^2+366623/14*x-77905,1375/14*x^3+1083*x^2-323215/7*x-219384,-2549/14*x^3-1545*x^2+433145/7*x+588170,142/7*x^3+1820*x^2+4988/7*x-937920,55*x^3-1510*x^2-69486*x+701730,-835/28*x^3+18033/2*x^2+100455/14*x-3685179,3175/14*x^3+707*x^2-203115/7*x-95788,11409/28*x^3+4085/2*x^2-1669277/14*x-1369135,8105/28*x^3+10461/2*x^2-4102645/14*x-2283051,-3867/14*x^3-5735*x^2-131645/7*x+4437620,-4465/14*x^3-10437*x^2+1988645/7*x+3020006,-4463/2*x^3+3155*x^2+682259*x-2169750,-46275/28*x^3-5903/2*x^2+10719935/14*x+5216235,-11729/28*x^3+111275/2*x^2+3184373/14*x-12710515]]];

f[12,8]=[
[x+27, [-1,1], [0,-27,-378,-832,-2484,14870,-22302,-16300,-115128,157086,-16456,-149266,-241110,-443188,922752,-697626,870156,2067062,-1680748,-1070280,-2403334,2301512,4708692,4143690,-1622974]],
[x-27, [-1,-1], [0,27,270,1112,-5724,-4570,-36558,51740,22248,-157194,-103936,-94834,659610,-75772,405648,-1346274,-1303884,1833782,1369388,2714040,2868794,-1129648,5912028,-897750,13719074]]];

f[13,8]=[
[x-10, [-1], [10,-73,-295,1373,-7646,2197,-4147,-3186,-17784,-93322,-124484,273661,585816,-533559,-530055,-615288,-392514,1878064,-3971438,-3746601,2485802,-1264456,434308,5830810,-2045330]],
[x^2+19*x+6, [-1], [x,-3*x-6,11*x-72,-9*x-1090,622*x+5004,2197,2003*x+6348,-4582*x-32476,-6792*x-77736,-3544*x-36570,3496*x+53084,13135*x+206432,-41178*x-556626,-4357*x+73262,-4221*x-859362,104610*x+1516986,-45486*x-617196,78370*x+3082226,272038*x+1673660,-545931*x-5754150,-57000*x-3771142,516480*x+4869656,-163292*x-7601760,639712*x+10984794,615988*x-2943958]],
[x^4-15*x^3-270*x^2+3264*x+12880, [1], [x,-1/4*x^3-3/4*x^2+65*x+278,13/4*x^3+15/4*x^2-805*x-2292,-3/4*x^3-25/4*x^2+171*x+2052,-20*x^3+4888*x+10794,-2197,-477/4*x^3+33/4*x^2+27925*x+67572,123*x^3+493*x^2-31860*x-144186,173*x^3+351*x^2-43156*x-110016,-826*x^3-2358*x^2+203336*x+905658,3267/2*x^3+4801/2*x^2-397758*x-1366654,7425/4*x^3+11339/4*x^2-438489*x-1496276,891/2*x^3+2745/2*x^2-114662*x-323994,-14931/4*x^3-11737/4*x^2+876195*x+2702734,-5647/4*x^3+17475/4*x^2+313879*x+150300,6119/2*x^3+6237/2*x^2-757694*x-1634502,-4872*x^3-15900*x^2+1302856*x+5428626,-25047/2*x^3-3821/2*x^2+3007902*x+6699914,8253*x^3+7571*x^2-2083836*x-5611802,91247/4*x^3+86493/4*x^2-5433847*x-16278996,16059*x^3+28625*x^2-4054860*x-16716822,18180*x^3+19108*x^2-4556832*x-7602876,4237/2*x^3-41889/2*x^2-785154*x+3407442,-23725*x^3-30639*x^2+5524084*x+23559810,-68487*x^3-96965*x^2+17398908*x+49875370]]];

f[14,8]=[
[x+8, [1,1], [-8,-82,448,-343,2408,7116,2486,36482,-12880,-88094,282636,-214534,-140874,36464,716868,-56946,-2149862,3084360,-3034364,-106624,988930,3415896,-15142,174810,13506790]],
[x+66, [-1,1], [8,-66,-400,-343,40,-4452,36502,-46222,-105200,-126334,-170964,20954,318486,77744,703716,1603278,-1171894,-2068872,-994268,33280,-2971454,-2376168,-2122358,6920346,4952710]],
[x^2-70*x-744, [-1,-1], [8,x,-9*x+378,343,-126*x+2700,189*x-9814,-90*x-16086,243*x-30184,-252*x+53784,2394*x-4002,-594*x-51016,9450*x-466666,-6174*x+248514,-378*x+777212,17442*x-367752,6552*x-302178,1107*x-2130576,-23193*x+671426,-34020*x+4026524,-21924*x+457704,14148*x+1474634,-106596*x+6059168,-135009*x+5343240,-74160*x-6025110,38934*x-1733158]]];

f[15,8]=[
[x+13, [1,1], [-13,-27,-125,1380,-3304,8506,-9994,41236,84120,132802,-55800,228170,-139670,-755492,836984,1641650,-989656,-1658162,-4523844,-389408,5617330,3901080,-9394116,2803746,5099426]],
[x+22, [-1,1], [-22,27,-125,-420,-2944,-11006,-16546,-25364,-5880,163042,-201600,120530,-115910,-19148,841016,501890,-1586176,-372962,4561044,1512832,-1522910,4231920,-1854204,-6888174,3700034]],
[x^2-7*x-138, [-1,-1], [x,27,125,-56*x+848,-464*x+3348,824*x-7378,-1400*x+2154,-2056*x-17596,5208*x+27696,8288*x+61878,-2168*x+159704,14424*x-301642,21392*x+240714,7136*x+151844,-5912*x-213048,-13232*x-237714,149776*x-380604,-1456*x-1251994,-129920*x-2082196,-76480*x-1606728,388208*x-2097334,80440*x-2595400,91872*x-3358020,-20496*x+8329914,-428640*x+2861954]]];

f[16,8]=[
[x+44, [1], [0,-44,430,1224,3164,6118,-16270,5476,-1576,122838,-251360,-52338,-319398,-710788,-284112,296062,897548,-884810,-4659692,2710792,-5670854,5124176,1563556,11605674,10931618]],
[x-84, [1], [0,84,-82,456,2524,-10778,-11150,-4124,-81704,99798,40480,-419442,141402,690428,682032,1813118,966028,1887670,-2965868,2548232,-1680326,-4038064,5385764,-6473046,-6065758]],
[x+12, [-1], [0,-12,-210,-1016,-1092,1382,14706,39940,-68712,-102570,-227552,160526,10842,630748,-472656,-1494018,-2640660,827702,126004,1414728,980282,3566800,-5672892,-11951190,8682146]]];

f[17,8]=[
[x+2, [-1], [-2,18,-10,-902,-8634,10858,4913,-784,77330,-18210,-237002,230878,-304182,-525032,802752,152862,-1602408,-2601610,1074604,-502298,3648258,-2892174,728104,7931846,-6551038]],
[x^3-x^2-304*x+1692, [-1], [x,-1/4*x^2-17/4*x+47/2,2*x^2+6*x-474,-35/4*x^2-259/4*x+2557/2,-119/4*x^2-743/4*x+15897/2,173/2*x^2+1925/2*x-22897,4913,-607/2*x^2-2447/2*x+59525,-307/4*x^2+1773/4*x-99027/2,574*x^2-8934*x-188706,9275/4*x^2+69051/4*x-821381/2,517*x^2+12273*x-395500,268*x^2+372*x+202074,3311/2*x^2-19793/2*x+6851,-5769*x^2-40705*x+707862,-2012*x^2-8420*x+673950,7295/2*x^2+192255/2*x-315453,719*x^2-8757*x+53504,512*x^2+95920*x-1753060,62483/4*x^2+232019/4*x-1914429/2,5045*x^2-269739*x-786076,-212783/4*x^2-1855567/4*x+22600033/2,-75015/2*x^2+150329/2*x+7892229,66073/2*x^2-217503/2*x-4662009,7400*x^2-335640*x-5674030]],
[x^6-15*x^5-514*x^4+5312*x^3+83552*x^2-422208*x-4272768, [1], [x,119/214848*x^5-2237/214848*x^4-6559/35808*x^3+18353/6714*x^2+21449/1492*x-40069/373,-13/11936*x^5+119/11936*x^4+3115/5968*x^3-1773/373*x^2-25063/746*x+176304/373,-51/23872*x^5-1599/23872*x^4+23353/11936*x^3+22827/746*x^2-445501/1492*x-917983/373,551/23872*x^5-3437/23872*x^4-106205/11936*x^3-34055/746*x^2+1218257/1492*x+4402887/373,21/11936*x^5-4783/11936*x^4+30317/5968*x^3+59101/373*x^2-868945/746*x-4967326/373,-4913,-119/11936*x^5-27603/11936*x^4+249445/5968*x^3+314363/373*x^2-6319193/746*x-28768138/373,-7933/23872*x^5+311567/23872*x^4+390391/11936*x^3-3470459/746*x^2+11717069/1492*x+129390723/373,4501/11936*x^5-121999/11936*x^4-590051/5968*x^3+1185877/373*x^2+5509951/746*x-45539760/373,-25823/23872*x^5+491397/23872*x^4+4553389/11936*x^3-4853929/746*x^2-34295617/1492*x+180834233/373,32123/11936*x^5-502929/11936*x^4-4847445/5968*x^3+3138247/373*x^2+28620281/746*x-26376664/373,2423/1492*x^5-6399/1492*x^4-354034/373*x^3-379916/373*x^2+51063552/373*x+99789378/373,-36861/11936*x^5+585551/11936*x^4+6869335/5968*x^3-3565515/373*x^2-90360979/746*x+36630038/373,13377/5968*x^5-319395/5968*x^4-3476879/2984*x^3+7613078/373*x^2+63898491/373*x-457939680/373,-29215/5968*x^5+1030645/5968*x^4+2794645/2984*x^3-24000034/373*x^2+24565655/373*x+1816772790/373,-163231/11936*x^5+2395589/11936*x^4+33714029/5968*x^3-19376497/373*x^2-400340481/746*x+503864322/373,158229/11936*x^5-3495887/11936*x^4-25204099/5968*x^3+30912117/373*x^2+172423263/746*x-1316911252/373,20003/5968*x^5+266791/5968*x^4-9594053/2984*x^3-8260786/373*x^2+198242217/373*x+1414535384/373,405879/23872*x^5-6511821/23872*x^4-75994197/11936*x^3+60373649/746*x^2+602936585/1492*x-2027477517/373,-8010/373*x^5+101326/373*x^4+3519580/373*x^3-29231120/373*x^2-331520640/373*x+1375418330/373,-387585/23872*x^5+7260219/23872*x^4+48707555/11936*x^3-39520487/746*x^2+121856049/1492*x+306076559/373,-186137/11936*x^5+4019683/11936*x^4+21856667/5968*x^3-33154895/373*x^2-31978407/746*x+1601021262/373,195279/11936*x^5-6598221/11936*x^4-2502177/5968*x^3+52483099/373*x^2-548587179/746*x-3400708914/373,-346805/5968*x^5+9326919/5968*x^4+52518519/2984*x^3-195798142/373*x^2-488597939/373*x+12050374682/373]]];

f[18,8]=[
[x+8, [1,-1], [-8,0,114,-1576,-7332,-3802,6606,24860,-41448,41610,33152,-36466,639078,-156412,433776,-786078,-745140,-1660618,-3290836,-5716152,2659898,3807440,-2229468,-5991210,-4060126]],
[x-8, [-1,-1], [8,0,210,1016,-1092,1382,-14706,-39940,-68712,102570,227552,160526,-10842,-630748,-472656,1494018,-2640660,827702,-126004,1414728,980282,-3566800,-5672892,11951190,8682146]]];

f[19,8]=[
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f[39,8]=[
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f[40,8]=[
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f[41,8]=[
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