Sharedwww / Tables / eigen_k10_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(99,10);

f[2,10]=[
[x-16, [-1], [16,-156,870,-952,-56148,178094,-247662,315380,204504,-3840450,-1309408,4307078,1512042,33670604,-10581072,16616214,112235100,-33197218,-121372252,-387172728,255240074,492101840,-457420236,-31809510,-673532062]]];

f[3,10]=[
[x+36, [1], [-36,-81,-1314,-4480,1476,-151522,108162,593084,-969480,-6642522,7070600,-7472410,-4350150,-4358716,28309248,16111710,-86075964,32213918,99531452,-44170488,-23560630,-401754760,-744528708,769871034,907130882]],
[x-18, [-1], [18,81,-1530,9128,21132,31214,-279342,144020,-1763496,4692510,-369088,9347078,-7226838,-23147476,22971888,78477174,-20310660,-179339938,274528388,-36342648,-247089526,191874800,-276159276,-678997350,-567657502]]];

f[4,10]=[
[x, [-1], [0,228,-666,-6328,-30420,-32338,590994,34676,1048536,4409406,-7401184,10234502,18352746,-252340,-49517136,-66396906,-61523748,35638622,181742372,90904968,-262978678,-116502832,-9563724,611826714,-259312798]]];

f[5,10]=[
[x+8, [1], [-8,-114,-625,4242,-46208,-115934,494842,-1008740,-532554,4196390,-3365028,-14931358,11056262,-6396794,-35559158,39738586,-85185620,45748642,-45286158,-189967468,412170946,95040840,261706326,-19938630,-19503358]],
[x^2+10*x-984, [-1], [x,-2*x+120,625,-214*x-220,1900*x+21492,-1352*x+50750,12856*x+270690,-2840*x-162460,19398*x-427620,-106960*x-2368290,154700*x+1580072,205296*x-9534490,-155800*x-14257638,25798*x+26573840,-523334*x+26589420,1137448*x-13830330,-1544720*x-35221380,-692000*x-140749858,2416706*x+11924240,-6278500*x-34957968,-8830952*x+16274330,18775640*x+97316960,-2748402*x+687432360,-13381680*x+348135930,2622216*x+332308370]]];

f[6,10]=[
[x+16, [1,-1], [-16,81,2694,-3544,29580,-44818,-101934,-895084,-1113000,-2357346,175808,-2919418,26218794,-18762964,-20966160,57251574,33587580,82260830,-188455804,80924040,-236140918,526909808,18346452,690643098,-438251038]]];

f[7,10]=[
[x^2+6*x-184, [1], [x,-11*x-76,95*x-834,-2401,3326*x+27636,-10899*x-45962,-9426*x-260238,1887*x-457052,38088*x+503328,94682*x-4717746,161430*x+1717920,248130*x+16112166,860818*x-6969270,-1048278*x-1112284,-1033182*x-44197056,-4685568*x-41651610,-1563825*x-8226084,3395319*x+32344150,7026216*x-99882020,-15075900*x+58019208,2840484*x-241055142,-16873716*x+183646400,21562275*x+286698804,-1406968*x+313912794,-5731530*x-833552622]],
[x^3-21*x^2-1326*x+19080, [-1], [x,-1/7*x^2+15/7*x+1122/7,-13/7*x^2-197/7*x+18408/7,2401,94*x^2-1402*x-88248,-25*x^2-2817*x+38900,1574/7*x^2-33802/7*x+986106/7,2437/7*x^2+88101/7*x-2609266/7,-544*x^2+28552*x+989544,2702*x^2-76482*x-889782,-70302/7*x^2+172530/7*x+77969012/7,8646*x^2-278586*x-6498718,-18842*x^2+314214*x+12419718,9338*x^2-196686*x-28794400,83238/7*x^2+3077542/7*x-131555412/7,-64336*x^2-1038688*x+96102102,-49659/7*x^2+16015637/7*x-160287930/7,-844773/7*x^2+2634435/7*x+1299929216/7,6816*x^2-3994344*x-64125484,-75180*x^2-2897916*x+196634160,118516/7*x^2+65865780/7*x+219913934/7,239916*x^2+5556204*x-606384376,-282481*x^2+6739407*x-122776998,1815976/7*x^2+59756920/7*x-1107997914/7,-123550*x^2-32288382*x+137565974]]];

f[8,10]=[
[x+60, [1], [0,-60,-2074,-4344,93644,-12242,-319598,-553516,-712936,2075838,-6420448,-18197754,9033834,19594732,-18484176,10255766,121666556,-45948962,50535428,267044680,-176213366,-269685680,-227032556,72141594,228776546]],
[x-68, [-1], [0,68,1510,10248,3916,-176594,148370,499796,-1889768,-920898,1379360,5064966,-24100758,25785196,-60790224,29496214,51819388,33426910,144856196,68397128,168216202,235398736,-64639852,-78782694,-24113566]]];

f[9,10]=[
[x, [1], [0,0,0,-12580,0,118370,0,-976696,0,0,1691228,-15384490,0,-16577080,0,0,0,-117903058,112542320,0,296368310,-616732324,0,0,1288928270]],
[x+18, [-1], [-18,0,1530,9128,-21132,31214,279342,144020,1763496,-4692510,-369088,9347078,7226838,-23147476,-22971888,-78477174,20310660,-179339938,274528388,36342648,-247089526,191874800,276159276,678997350,-567657502]],
[x-36, [-1], [36,0,1314,-4480,-1476,-151522,-108162,593084,969480,6642522,7070600,-7472410,4350150,-4358716,-28309248,-16111710,86075964,32213918,99531452,44170488,-23560630,-401754760,744528708,-769871034,907130882]]];

f[10,10]=[
[x-46, [1,1], [-16,46,-625,-10318,-5568,45986,-381318,610460,-1447914,5385510,3053852,12889442,-33786618,-36886234,-44163798,29746266,-65575380,40183202,-115706158,-231681708,358691906,-486017080,251168886,-526039110,-1075981438]],
[x+204, [1,-1], [-16,-204,625,5432,73932,-114514,41682,1057460,1599336,2184510,-9619648,4799942,9531882,-13464484,11441952,53615766,81862620,-104691298,140571092,97098792,171848906,-117380080,323637636,-894379110,232678562]],
[x-16, [-1,1], [16,174,-625,4658,28992,-164446,-594822,-295780,2544534,-3722970,2335772,10840418,21593862,10832294,5172138,98179674,16162860,-43928158,-81557422,161307732,-247147966,-583345720,-14571786,470133690,-117838462]]];

f[11,10]=[
[x^3-1224*x+6688, [1], [x,-1/8*x^2-11/2*x+40,-3/8*x^2-77/2*x-302,11/4*x^2+155*x-4664,-14641,-363/4*x^2-1627*x+42966,-539/2*x^2+5920*x+226138,-1969/2*x^2+1448*x+460900,23639/8*x^2-7667/2*x-1852948,7711/4*x^2-33483*x-2470930,4231/8*x^2-62403/2*x-1939996,-73373/8*x^2-582483/2*x+4543978,-6523/4*x^2-167259*x-1926342,204875/4*x^2+676181*x-35529252,-5705*x^2+1312520*x-5729992,112551/2*x^2-886226*x-30087434,-264531/8*x^2+1483383/2*x+137694952,-768383/4*x^2-287285*x+140406222,1419385/8*x^2-4403685/2*x-34590576,-2085075/8*x^2-1204489/2*x+193399300,1275527/4*x^2-1934789*x-413146470,1346323/4*x^2-10780131*x-540952808,-1038081/4*x^2+2165781*x+625030164,-10415009/8*x^2-5283663/2*x+829156462,3441005/8*x^2+24838363/2*x-1086794514]],
[x^5-16*x^4-1506*x^3+6428*x^2+619552*x+4247232, [-1], [x,1/312*x^4-1/12*x^3-571/156*x^2+787/13*x+14127/13,-29/1560*x^4+9/20*x^3+837/52*x^2-44354/195*x-163411/65,7/78*x^4-7/2*x^3-1120/13*x^2+92953/39*x+415030/13,14641,9/26*x^4-7/2*x^3-2604/13*x^2-3365/13*x-573628/13,-133/52*x^4+83*x^3+54545/26*x^2-741685/13*x-7556802/13,-823/156*x^4+151*x^3+196745/26*x^2-5337071/39*x-36808376/13,-1003/312*x^4+305/4*x^3+295043/52*x^2-2662663/39*x-20609321/13,-9829/156*x^4+3087/2*x^3+1991773/26*x^2-42586898/39*x-286291192/13,1189/312*x^4+3233/4*x^3-468973/52*x^2-30899639/39*x-12147185/13,18497/312*x^4-11277/4*x^3-3895117/52*x^2+93738434/39*x+471675147/13,-12845/78*x^4+5533/2*x^3+2874304/13*x^2-69462659/39*x-807398680/13,45835/156*x^4-16415/2*x^3-7789055/26*x^2+179128460/39*x+1162798362/13,29/2*x^4-542*x^3-83953*x^2+2175754*x+51402600,-13291/39*x^4+15631*x^3+3244320/13*x^2-434319842/39*x-1325550430/13,-7383/8*x^4+121367/4*x^3+3999717/4*x^2-22130265*x-325855047,225253/156*x^4-79367/2*x^3-38182477/26*x^2+995677130/39*x+5803842132/13,-31265/24*x^4+128955/4*x^3+5093249/4*x^2-53056343/3*x-231344243,-14947/8*x^4+281843/4*x^3+8745177/4*x^2-55095885*x-839390535,-42466/39*x^4+36423/2*x^3+12722111/13*x^2-55753391/39*x-1332512588/13,-555121/156*x^4+255917/2*x^3+88460573/26*x^2-3594583796/39*x-15701632298/13,-150847/156*x^4-10115/2*x^3+39548775/26*x^2-330401654/39*x-2656237078/13,-2884591/312*x^4+872115/4*x^3+513549523/52*x^2-5127396910/39*x-30374557649/13,1548005/104*x^4-1841999/4*x^3-875883563/52*x^2+4637111316/13*x+70085015225/13]]];

f[12,10]=[
[x, [-1,1], [0,-81,990,8576,70596,-2530,-200574,-695620,2472696,5474214,3732104,-21898522,-23818950,10612676,2398464,-8994978,-143417916,-19804258,-165625156,-194801400,148729418,-30134152,302054076,909502650,-872463358]]];

f[13,10]=[
[x^4+33*x^3-1194*x^2-24936*x+232000, [1], [x,-1/664*x^3-129/664*x^2-947/332*x+6202/83,55/664*x^3+1119/664*x^2-35231/332*x-48120/83,-303/664*x^3-5887/664*x^2+121419/332*x-94368/83,-139/83*x^3+3483/83*x^2+271088/83*x-4380918/83,-28561,15621/664*x^3+188445/664*x^2-6359629/332*x+6768792/83,-2967/166*x^3-66347/166*x^2+2192661/83*x+21852678/83,-22171/166*x^3-814275/166*x^2+9600187/83*x+124896816/83,173*x^3+8793*x^2-75910*x-5250318,77355/332*x^3+91171/332*x^2-61773531/166*x-126913022/83,240723/664*x^3+4559003/664*x^2-223064955/332*x-262415176/83,-4803/332*x^3+2744901/332*x^2-14447021/166*x-392325222/83,-481131/664*x^3-33877771/664*x^2-29745441/332*x+1734464906/83,1669997/664*x^3+40767069/664*x^2-625628257/332*x-1661484600/83,-416899/332*x^3+3017925/332*x^2+514133299/166*x-4150851618/83,571755/83*x^3+9571665/83*x^2-761160316/83*x-4575026478/83,318411/332*x^3+43585603/332*x^2+326097573/166*x-4948931378/83,-790389/166*x^3-59323081/166*x^2+28814379/83*x+17328461798/83,-1262293/664*x^3+89769723/664*x^2+3281578729/332*x-876720288/83,-630543/166*x^3-30694111/166*x^2+739340451/83*x+25521083262/83,-377928/83*x^3+26369924/83*x^2+956580996/83*x-20119013772/83,-4387943/332*x^3-67449039/332*x^2+677201679/166*x-5957605542/83,-2198611/166*x^3+69917349/166*x^2+209639339/83*x-74370639450/83,-9825573/166*x^3-310826309/166*x^2+4672960713/83*x+97974616430/83]],
[x^5-15*x^4-1348*x^3+8508*x^2+383520*x-1249344, [-1], [x,1/1088*x^4-67/1088*x^3+29/136*x^2+10467/272*x-17547/68,7/1088*x^4-197/1088*x^3-1055/136*x^2+38589/272*x+148899/68,79/1088*x^4-1485/1088*x^3-9065/136*x^2+114525/272*x+596395/68,207/544*x^4-8157/544*x^3-14295/68*x^2+1012165/136*x+787635/34,28561,331/64*x^4-9105/64*x^3-27563/8*x^2+912137/16*x-452697/4,113/32*x^4-4611/32*x^3-9333/4*x^2+619371/8*x+114493/2,-545/34*x^4+18665/34*x^3+174661/17*x^2-5176048/17*x-4888632/17,-1215/34*x^4+44515/34*x^3+414909/17*x^2-11724004/17*x+4353246/17,1101/34*x^4-7176/17*x^3-1142767/34*x^2+1619307/17*x+113857936/17,-156053/1088*x^4+3713487/1088*x^3+17523837/136*x^2-391912119/272*x-948705353/68,146791/544*x^4-5267845/544*x^3-8520635/68*x^2+648184333/136*x-633988689/34,-5009/64*x^4+5043/64*x^3+927483/8*x^2+24617997/16*x-102880261/4,-19709/64*x^4+1020567/64*x^3+173515/8*x^2-139821639/16*x+300566415/4,6297/32*x^4-261627/32*x^3+747/4*x^2+18837171/8*x-75713391/2,-14463/32*x^4-57907/32*x^3+2318955/4*x^2+18205243/8*x-48674259/2,-93943/544*x^4+3451509/544*x^3+7059459/68*x^2-52154397/136*x-1232849551/34,-41681/32*x^4+1564611/32*x^3+2474913/4*x^2-202033755/8*x+14358739/2,-1790803/1088*x^4+66957401/1088*x^3+154468133/136*x^2-7846244009/272*x-4707568191/68,27493/34*x^4-2729193/34*x^3+13266805/17*x^2+795446892/17*x-8330747654/17,43085/17*x^4-1293132/17*x^3-26736299/17*x^2+547450758/17*x-4892145824/17,1345/16*x^4+69157/16*x^3-875536*x^2+17130351/4*x+756753897,-6511*x^4+167055*x^3+5400886*x^2-69011336*x-669832950,-2045873/272*x^4+84300051/272*x^3+52336155/34*x^2-11163182067/68*x+25490050621/17]]];

f[14,10]=[
[x+6, [1,1], [-16,-6,560,-2401,-54152,-113172,6262,257078,-266000,1574714,-4637484,-11946238,21909126,27520592,52927836,16221222,-140509618,-202963560,153734572,279655936,-404022830,-130689816,420134014,-469542390,-872501690]],
[x-16, [-1,1], [16,170,544,-2401,48824,-15876,-21418,-716410,-2470000,5556826,5799348,-3894430,-6360858,-18701296,56539068,-59894682,165629662,51419016,93546508,-95633536,306496402,496474152,-371486962,-165482550,758016742]],
[x^2+14*x-57576, [1,-1], [-16,x,21/5*x-6678/5,2401,210*x+23940,-45*x+49826,-318*x-437430,2691*x+273224,1428*x+49896,-23898*x+835878,-7866*x+1039304,-28602*x-10562002,-103578*x+8783250,69174*x+2581076,-40086*x-37551864,92904*x-969546,223947*x-65253552,173241*x+115113530,330876*x+168781268,-1264788*x-92846376,-1208628*x-30802534,442764*x+137920736,1215087*x-83047272,-1357008*x+386329818,2797938*x+17500826]]];

f[15,10]=[
[x-22, [1,1], [22,-81,-625,-5988,-14648,37906,-441098,441820,2264136,-1049350,-7910568,-20992558,13285562,-23130764,-13873688,-57635174,-32042120,110664022,-118568268,276679712,-264023294,448202760,851015796,189894930,-1014149278]],
[x+4, [-1,-1], [-4,81,625,-7680,-86404,-149978,-207622,716284,1369920,-3194402,-2349000,18735710,-29282630,-1516724,615752,4747430,60616076,-126745682,-111182652,-175551608,-61233350,234431160,118910388,-316534326,242912258]],
[x^2-31*x-302, [1,-1], [x,-81,625,224*x+3584,-2368*x+25948,-5344*x+94974,7520*x-195038,-5728*x+40836,26272*x-774848,-168576*x+1273822,-152736*x+7758624,-198496*x+14060854,-492096*x+20657674,-702336*x+7290628,1970528*x-46333304,-177728*x+4320342,-4348352*x+49652124,950208*x+156020446,1026560*x-160009588,-4545280*x+175594872,1168192*x-134438518,19049120*x-307638880,7260288*x-298575540,9049152*x-354081414,-13450880*x+1094318082]],
[x^2-19*x-1092, [-1,1], [x,81,-625,-56*x-5404,-1952*x+36288,-1384*x+84986,2200*x+171678,968*x-210844,-64968*x+729048,12416*x-155238,75736*x-3233056,-174696*x+4346426,470096*x+2639754,152384*x+12426812,431368*x+43885224,929872*x-40986582,-1613408*x+109258944,-2256688*x+98478566,-7444160*x+87515708,7061120*x-181216128,-6480208*x+45000818,-1798040*x-449122000,3161088*x+73489740,-9306192*x+200667906,44039040*x-224803582]]];

f[16,10]=[
[x-60, [1], [0,60,-2074,4344,-93644,-12242,-319598,553516,712936,2075838,6420448,-18197754,9033834,-19594732,18484176,10255766,-121666556,-45948962,-50535428,-267044680,-176213366,269685680,227032556,72141594,228776546]],
[x+68, [1], [0,-68,1510,-10248,-3916,-176594,148370,-499796,1889768,-920898,-1379360,5064966,-24100758,-25785196,60790224,29496214,-51819388,33426910,-144856196,-68397128,168216202,-235398736,64639852,-78782694,-24113566]],
[x-156, [-1], [0,156,870,952,56148,178094,-247662,-315380,-204504,-3840450,1309408,4307078,1512042,-33670604,10581072,16616214,-112235100,-33197218,121372252,387172728,255240074,-492101840,457420236,-31809510,-673532062]],
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f[17,10]=[
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f[26,10]=[
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f[27,10]=[
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f[28,10]=[
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f[33,10]=[
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