Sharedwww / Tables / eigen_k12_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(99,12);

f[1,12]=[
[x+24, [], [-24,252,4830,-16744,534612,-577738,-6905934,10661420,18643272,128406630,-52843168,-182213314,308120442,-17125708,2687348496,-1596055698,-5189203740,6956478662,-15481826884,9791485272,1463791322,38116845680,-29335099668,-24992917110,75013568546]]];

f[3,12]=[
[x-78, [1], [78,-243,-5370,-27760,637836,766214,3084354,-19511404,15312360,10751262,-50937400,664740830,898833450,-957947188,-1555741344,3792417030,555306924,4950420998,5292399284,-14831086248,13971005210,3720542360,8768454036,-25472769174,-39092494846]]];

f[4,12]=[
[x, [-1], [0,-516,-10530,49304,-309420,-1723594,-2279502,4550444,-7282872,-69040026,-141740704,711366974,-1225262214,-33606220,123214608,1106121582,-9062779932,-3854150458,-15313764676,20619626328,-2063718694,13689871472,65570428908,-29715508854,-23439626206]]];

f[5,12]=[
[x-34, [-1], [34,-792,3125,-17556,-468788,-374042,-3724286,-379460,-32458092,69696710,171448632,-291340546,191343242,-1759857392,1623469924,-644888642,925569220,-10898589338,3795674064,-22966943728,9880820458,-20768886240,3204862008,63176321130,126494473874]],
[x^2+20*x-5336, [1], [x,16/3*x-170/3,-3125,176*x+30710,-8800*x-397088,-4288*x+1664250,42176*x+1080730,91520*x+3577860,11152*x+29583490,766080*x+54730990,-2402400*x+98247732,6344576*x+73947370,-7550400*x-448375658,-4636368*x+268611370,-6835024*x-769381010,-62251328*x-53352990,58605760*x+4244815380,-17856000*x-936772838,-30563824*x+7561506830,-18268000*x+16286555772,113205952*x-13859364910,-191878720*x-3570198760,-366939408*x+2980157130,-485093760*x-11188323030,1515290176*x+13612549890]]];

f[6,12]=[
[x+243, [1,1], [-32,-243,5766,72464,-408948,1367558,5422914,15166100,-52194072,118581150,-57652408,-375985186,856316202,-1245189172,-1306762656,409556358,-2882866260,5731767302,3893272244,-9075890088,-15571822822,-30196762600,23135252628,-25614819990,-61937553406]],
[x-243, [1,-1], [-32,243,-11730,-50008,-531420,1332566,-5109678,2901404,30597000,-77006634,-239418352,-785041666,411252954,351233348,95821680,-1465857378,5621152020,-10473587770,4515307532,-8509579560,2012496986,-22238409568,6328647516,-50123706678,94805961314]],
[x-32, [-1,-1], [32,243,3630,32936,-758748,-2482858,8290386,-10867300,20539272,28814550,150501392,-319891714,-368008998,620469572,2763110256,-268284258,1672894740,-7787197498,18706694156,-8346990888,19641746522,-5873807200,8492558172,75527864010,-82356782494]]];

f[7,12]=[
[x^2+54*x-2640, [-1], [x,-6*x-102,10*x-6480,16807,4160*x-263088,29862*x+801500,-3100*x+1996326,-78138*x-11109082,-39500*x-34147008,-1928052*x-21299598,-1370844*x-44653564,-5698188*x-417460246,-1231356*x-122384682,9186912*x+1161419240,38136388*x+1313802828,-64945144*x-3846427074,-104471170*x-1265049090,56906874*x+9057783128,203009004*x+10409505092,60930912*x-10510871040,199184616*x-10067016334,-434987496*x-10748260264,-334983474*x-6406046514,-390416072*x-61311890358,203366268*x-90623421322]],
[x^3-77*x^2-2854*x+225104, [1], [x,-11/21*x^2+103/7*x+33758/21,59/7*x^2-517/7*x-203864/7,-16807,-242*x^2+9614*x+345608,111*x^2-10449*x-789452,13966/7*x^2-556530/7*x-3029398/7,-16027/7*x^2+374949/7*x+81339206/7,-26368*x^2-271104*x+111665392,94206*x^2-1334914*x-373446750,-528982/7*x^2+20757546/7*x+1897574692/7,214134*x^2-1636362*x-599585382,-480098*x^2-4531682*x+2276507558,-263494*x^2+8794170*x+949775472,-5512434/7*x^2+126235278/7*x+24498285900/7,1709072*x^2-9570288*x-6352710722,6211549/7*x^2-324290787/7*x-2006394706/7,53985851/7*x^2-1091697669/7*x-176474991136/7,7965200*x^2-165057264*x-35669636140,-6546092*x^2+15923796*x+30504930080,-7137500/7*x^2-1827776988/7*x+88685181038/7,3959276*x^2+121951980*x-36786471336,8490007*x^2+96511959*x+5777190530,257804312/7*x^2-1145562088/7*x-1184466458570/7,-31507574*x^2-316246518*x+106589168630]]];

f[8,12]=[
[x+36, [-1], [0,-36,-3490,-55464,-597004,1373878,10140850,-7297396,-32057464,-13605402,233160800,-257786178,-221438598,-1697758892,527509392,3277379822,-3001908988,-11630023610,-17189000548,26169539608,-7039021094,-4199910416,-39739936436,10565331594,-69851645662]],
[x^2-56*x-445680, [1], [0,x,-12*x+4270,42*x+44352,-693*x+98944,948*x+498694,-10824*x+1018514,-4587*x-10804864,-24738*x+18596032,59556*x-116081418,-28632*x+33162752,-81564*x+40063182,647088*x+582488634,324051*x-31833344,-816420*x-591679872,3514980*x-2002694402,4307463*x-3127072256,4588692*x+4766413078,-21317583*x+7948439936,-20099142*x+2722771520,-3259368*x+5619082042,41373444*x+24820355200,-13552251*x-53734524928,90758808*x+33052899306,-64199400*x+947679362]]];

f[9,12]=[
[x-24, [-1], [24,0,-4830,-16744,-534612,-577738,6905934,10661420,-18643272,-128406630,-52843168,-182213314,-308120442,-17125708,-2687348496,1596055698,5189203740,6956478662,-15481826884,-9791485272,1463791322,38116845680,29335099668,24992917110,75013568546]],
[x+78, [-1], [-78,0,5370,-27760,-637836,766214,-3084354,-19511404,-15312360,-10751262,-50937400,664740830,-898833450,-957947188,1555741344,-3792417030,-555306924,4950420998,5292399284,14831086248,13971005210,3720542360,-8768454036,25472769174,-39092494846]],
[x^2-2520, [1], [x,0,224*x,58100,-3200*x,762650,-178752*x,-10301704,207104*x,-2808800*x,106159508,-9574450,-2161600*x,1590697400,-28695296*x,20943648*x,-115091200*x,-3092621098,-9113820400,66739200*x,620142950,10618486484,1195288192*x,-1223376000*x,131872902350]]];

f[10,12]=[
[x-738, [1,1], [-32,738,-3125,25574,769152,-918982,10312794,-5521660,-39973422,-15269010,-241583788,-25751446,-1217700138,-683436262,1537395294,3572891298,-1069039020,-2091535078,-1462369186,9660178332,-5603447662,5026936280,-38405955462,35558583210,10572232514]],
[x+12, [1,-1], [-32,-12,3125,-14176,-756348,-905482,2803794,-5428660,-10236672,-197498010,-44362288,576737054,930058362,1605598988,-1803684456,1558674798,-9501997020,6736320422,8402906564,-4806306168,7462713338,-20644540720,-68013349212,69871323210,39960952514]],
[x+318, [-1,1], [32,-318,-3125,-70714,238272,-2097478,5955546,10210820,-3535758,-139304850,-101002348,-524913814,284590422,-1253635078,-216106434,-4881275358,8692473300,3296491802,18275027966,-13287447588,-32505250798,9297455960,-22741484838,-93378882390,-5811134014]],
[x^2-604*x-105696, [-1,-1], [32,x,3125,-177*x+60500,-1254*x+589500,1452*x+426758,-5028*x-1643358,7404*x-16684708,39081*x-34420500,-107592*x+61605894,113442*x-13552792,303192*x+97063742,-1168812*x-39654294,-986667*x-428520184,2086863*x-1274296500,9183012*x-2788515042,1261416*x+3957603588,22983984*x-6383413786,22637439*x-13173391432,-7768566*x+9246023424,-29730708*x+57634058,30074724*x-15401031808,77912265*x-2536259568,-35835480*x+17426684970,175966980*x-84035759374]]];

f[11,12]=[
[x^3-4500*x+92224, [-1], [x,-4/17*x^2-110/17*x+9773/17,90/17*x^2+1540/17*x-311395/17,-440/17*x^2-21110/17*x+1291202/17,161051,5808/17*x^2+285214/17*x-31217868/17,-16280/17*x^2-1585306/17*x+117475358/17,142340/17*x^2+6247090/17*x-475699840/17,-231814/17*x^2+2070970/17*x+677668993/17,22616/17*x^2+9841380/17*x-2201018336/17,-257162/17*x^2+10468458/17*x-1003171727/17,644254/17*x^2+53096076/17*x-4507023193/17,-10552256/17*x^2-501007746/17*x+31443619416/17,8336680/17*x^2+225806680/17*x-24091114146/17,2025932/17*x^2-397133924/17*x-24111952376/17,2437860/17*x^2+389755652/17*x-24317849278/17,-15367764/17*x^2-1822155918/17*x+35658380327/17,-3263656/17*x^2+331317836/17*x-149409003876/17,45578896/17*x^2+5118166218/17*x-78283250517/17,104141754/17*x^2+8245253522/17*x-291441189277/17,197320288/17*x^2+7814945654/17*x-512530999068/17,-296828884/17*x^2-16700031144/17*x+844560681338/17,476487000/17*x^2+4821808500/17*x-1282076508306/17,-788014172/17*x^2-15544258884/17*x+2265757610711/17,115608236/17*x^2-6246508136/17*x-392070464343/17]],
[x^5-32*x^4-7718*x^3+140876*x^2+11993504*x-87564928, [1], [x,-1/36792*x^4-1/252*x^3+2503/6132*x^2+86591/4599*x-3160763/4599,17/36792*x^4-13/252*x^3-6689/2044*x^2+1427732/4599*x+12880711/4599,8/657*x^4-7/18*x^3-5441/73*x^2+975835/657*x+46021382/657,-161051,32/511*x^4-125/14*x^3-135651/511*x^2+13703225/511*x+579723628/511,1317/2044*x^4-557/7*x^3-3118603/1022*x^2+23084539/73*x+1742404642/511,29801/18396*x^4-4325/63*x^3-5181951/1022*x^2+655479625/4599*x-43211193520/4599,45197/5256*x^4-10507/36*x^3-15702297/292*x^2+447590537/657*x+17971883011/657,-9073/2628*x^4-7825/18*x^3-1644835/146*x^2+2234117950/657*x+55945794080/657,-84989/36792*x^4+32125/36*x^3+41592745/2044*x^2-20018957825/4599*x+49144107203/657,613769/5256*x^4-112165/36*x^3-215462169/292*x^2+3578302004/657*x+515613514747/657,-735838/4599*x^4+505175/126*x^3+614543829/511*x^2-1174757525/657*x-6325255039048/4599,-186305/2628*x^4-7643/18*x^3+59155905/146*x^2+12582106640/657*x-165926278430/657,216875/1022*x^4-63218/7*x^3-440260525/511*x^2+2457597682/73*x-317180601600/511,57404/657*x^4-97625/9*x^3-73699558/73*x^2+56231476378/657*x+2354639426066/657,-3230191/4088*x^4+689725/28*x^3+7585404675/2044*x^2-14307040525/511*x+625132811503/511,-3248345/18396*x^4+4428775/126*x^3-222714011/1022*x^2-917933681650/4599*x+13252222106068/4599,2263915/5256*x^4-1890257/36*x^3+563730985/292*x^2+162575065009/657*x-4607426792755/657,-1113989/584*x^4-313025/4*x^3+4937703777/292*x^2+35508397025/73*x-2272573619975/73,-11354249/9198*x^4+1719677/126*x^3+2384282974/511*x^2-14413679105/657*x+19561739689052/4599,1211099/2628*x^4-1916575/18*x^3+241581909/146*x^2+199346026600/657*x+678052160126/657,93353279/18396*x^4-26490049/126*x^3-23675421779/1022*x^2+372409813138/657*x-60457556610946/4599,348290879/36792*x^4-60115075/252*x^3-134859111535/2044*x^2+457337839700/657*x+210504567231697/4599,-5135215/4088*x^4+13921111/28*x^3-32021698865/2044*x^2-108711025914/73*x+41859851984255/511]]];

f[12,12]=[
[x+243, [-1,1], [0,-243,9990,-86128,-806004,-960250,-4306878,401300,17751528,-84704994,140930504,-413506594,150094890,706702028,-2475725472,1600124166,3945492396,-885973498,-4881597772,12631469400,1423335194,667407512,5716071828,-85738736790,-52302647806]],
[x-243, [-1,-1], [0,243,2862,9128,668196,2052950,1604178,-230500,-43012728,-141745194,233221904,278269694,-1181577510,856975172,-1664054928,-3851181666,10339000596,185948102,2915010572,12662314200,-15201270694,-36644027488,-9217637028,30573828810,145701815906]]];

f[13,12]=[
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f[26,12]=[
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f[27,12]=[
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