CoCalc Public Fileswww / tables / eigen_k6_N1-99_prec97.gp
Author: William A. Stein
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\\ 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(99,6);

f[3,6]=[
[x+6, [-1], [-6,9,6,-40,-564,638,882,-556,-840,4638,4400,-2410,-6870,9644,-18672,33750,-18084,39758,-23068,-4248,-41110,21920,82452,-94086,49442]]];

f[4,6]=[
[x, [-1], [0,-12,54,-88,540,-418,594,836,-4104,-594,4256,-298,17226,-12100,-1296,19494,-7668,-34738,21812,-46872,67562,-76912,67716,29754,-122398]]];

f[5,6]=[
[x-2, [-1], [2,-4,25,192,-148,286,-1678,1060,2976,-3410,-2448,182,-9398,-1244,-12088,23846,-20020,32302,60972,-32648,-38774,-33360,16716,101370,-119038]]];

f[6,6]=[
[x-4, [-1,1], [4,-9,-66,176,-60,-658,-414,956,600,5574,-3592,-8458,19194,13316,-19680,-31266,26340,-31090,-16804,6120,-25558,74408,-6468,-32742,166082]]];

f[7,6]=[
[x+10, [1], [-10,-14,-56,-49,232,-140,-1722,-98,1824,3418,-7644,-10398,-17962,10880,9324,2262,-2730,25648,-48404,-58560,68082,31784,-20538,-50582,-58506]],
[x^2-9*x+6, [-1], [x,-6*x+24,10*x-54,49,-124*x+756,126*x-742,-76*x+1242,-18*x-1552,568*x-1512,252*x+2214,540*x-2440,540*x+686,-1092*x+1890,-4788*x+20036,3748*x-11016,-208*x+5670,-2050*x-12744,-4806*x-10750,-1944*x+21140,-4200*x+67608,-5256*x+32378,14904*x-41440,15750*x-12096,-22208*x+142074,8820*x-29302]]];

f[8,6]=[
[x, [-1], [0,20,-74,-24,124,478,-1198,3044,184,-3282,-5728,10326,-8886,-9188,23664,11686,16876,-18482,-15532,-31960,-4886,44560,67364,71994,48866]]];

f[9,6]=[
[x-6, [-1], [6,0,-6,-40,564,638,-882,-556,840,-4638,4400,-2410,6870,9644,18672,-33750,18084,39758,-23068,4248,-41110,21920,-82452,94086,49442]]];

f[10,6]=[
[x+26, [1,1], [-4,-26,-25,-22,-768,-46,378,1100,-1986,-5610,-3988,-142,1542,-5026,24738,-14166,28380,5522,-24742,42372,-52126,-39640,-59826,57690,-144382]],
[x-24, [1,-1], [-4,24,25,-172,132,-946,-222,500,3564,2190,2312,-11242,1242,20624,6588,-21066,7980,16622,1808,-24528,20474,-46240,-51576,-110310,-78382]],
[x-4, [-1,1], [4,6,-25,-118,192,1106,762,-2740,1566,5910,-6868,-5518,-378,-2434,13122,-9174,-34980,-9838,33722,70212,21986,4520,-109074,38490,-1918]]];

f[11,6]=[
[x+4, [1], [-4,-15,-19,10,-121,-1148,686,-384,3709,-5424,-6443,12063,-1528,-4026,7168,-29862,-6461,-16980,29999,31023,1924,65138,-102714,17415,66905]],
[x^3-90*x+188, [-1], [x,-1/6*x^2-5/3*x+64/3,-3/2*x^2-7*x+98,5*x^2+10*x-272,121,-3*x^2+58*x+342,10*x^2+172*x-238,10*x^2-20*x-140,-167/2*x^2-355*x+3988,23*x^2-90*x-2522,-23/2*x^2-147*x-676,-197/2*x^2+543*x+11818,-47*x^2-1566*x+4818,185*x^2+1930*x-19836,212*x^2+248*x-18464,270*x^2+604*x+662,-249/2*x^2+2643*x+6224,673*x^2+1226*x-34218,907/2*x^2-4761*x-43128,891/2*x^2-2153*x-13636,587*x^2+7718*x-30078,-227*x^2+2994*x+55336,-1875*x^2-4350*x+64524,1523/2*x^2-2121*x-81298,-2143/2*x^2-4163*x+67518]]];

f[13,6]=[
[x^2+5*x+2, [1], [x,-6*x-29,40*x+79,-70*x-193,-84*x-398,-169,-128*x-1635,28*x-86,1416*x+2228,48*x-286,-448*x+2740,-1840*x-13029,-1952*x-960,4718*x+13005,-9670*x-19189,-6816*x-38900,8668*x+2202,9296*x+24232,-196*x-35454,-3666*x+24533,18560*x+83606,9736*x-3308,17920*x+6944,23504*x+117014,58720*x+129422]],
[x^3-7*x^2-84*x+444, [-1], [x,-1/4*x^2-3/4*x+45/2,-1/4*x^2-27/4*x+105/2,-3/4*x^2-9/4*x+79/2,15/2*x^2-67/2*x-279,169,-93/4*x^2+401/4*x+3501/2,-67/2*x^2+423/2*x+1979,38*x^2-110*x-1284,-146*x^2+202*x+7170,-67*x^2-81*x+4166,419/4*x^2-2223/4*x-26315/2,-125/2*x^2+1841/2*x-1293,697/4*x^2-2421/4*x-21029/2,-807/4*x^2+939/4*x+50931/2,1077/2*x^2+567/2*x-43803,-475/2*x^2+3391/2*x+34539,1165/2*x^2+2655/2*x-49483,-833/2*x^2+3789/2*x+44417,3127/4*x^2-5659/4*x-54771/2,-642*x^2-2070*x+36926,-894*x^2-1962*x+48620,1210*x^2+2598*x-60888,-108*x^2-8756*x+39474,125*x^2-1521*x+19952]]];

f[14,6]=[
[x+4, [1,-1], [-4,10,84,49,-336,584,-1458,470,-4200,4866,-7372,14330,6222,3704,-1812,-37242,34302,24476,-17452,28224,3602,42872,-35202,26730,-16978]],
[x-4, [-1,1], [4,8,10,-49,-340,-294,1226,2432,2000,-6746,8856,9182,-14574,8108,-312,-14634,-27656,34338,12316,36920,-61718,-64752,-77056,-8166,20650]]];

f[15,6]=[
[x+2, [1,1], [-2,-9,-25,-132,472,-686,-1562,-2180,264,170,7272,-142,-16198,-10316,18568,21514,34600,-35738,-5772,-69088,-70526,47640,74004,-90030,-33502]],
[x-7, [-1,1], [7,9,-25,12,112,-974,2182,1420,3216,-4150,-5688,6482,5402,-21764,-368,12586,-25520,11782,-13188,-35968,73186,-52440,69036,-33870,143042]],
[x^2+x-102, [1,-1], [x,-9,25,-16*x-64,-32*x+108,16*x+446,-80*x+978,208*x+836,-48*x-1632,-64*x+942,176*x+1424,-816*x+3926,-544*x-4086,64*x-8188,-1232*x-10296,2272*x-6042,3232*x+1164,-1568*x+9326,1280*x-5812,3200*x-18888,-608*x+29258,-3760*x+51920,-4032*x-63060,-7392*x+48186,12480*x-6142]]];

f[16,6]=[
[x+20, [1], [0,-20,-74,24,-124,478,-1198,-3044,-184,-3282,5728,10326,-8886,9188,-23664,11686,-16876,-18482,15532,31960,-4886,-44560,-67364,71994,48866]],
[x-12, [-1], [0,12,54,88,-540,-418,594,-836,4104,-594,-4256,-298,17226,12100,1296,19494,7668,-34738,-21812,46872,67562,76912,-67716,29754,-122398]]];

f[17,6]=[
[x-1, [1], [1,-18,-16,28,-138,82,-289,-2260,-3424,8304,-4580,5932,9990,-12776,-768,-12630,37968,18476,-51272,-10592,-70974,-25944,-63056,7706,99662]],
[x+6, [1], [-6,10,-72,-196,450,-142,-289,-244,2904,-6984,-436,-8572,16374,-19216,-19920,1146,22008,35780,23264,-31704,-13966,-51088,-64344,70650,62702]],
[x^4-3*x^3-94*x^2+284*x+968, [-1], [x,-1/24*x^3-11/24*x^2+7/2*x+163/6,1/2*x^3+1/2*x^2-39*x+22,-5/8*x^3-15/8*x^2+67/2*x+283/2,11/8*x^3+73/8*x^2-179/2*x-985/2,-19/4*x^3+35/4*x^2+308*x-519,289,15/4*x^3+133/4*x^2-323*x-529,-13/8*x^3+393/8*x^2+807/2*x-2837/2,15/2*x^3+119/2*x^2+107*x-4586,-147/8*x^3-1145/8*x^2+1941/2*x+14365/2,25*x^3+56*x^2-1687*x-1132,-56*x^3-162*x^2+2870*x+10806,121/4*x^3+979/4*x^2-1429*x-7287,31/2*x^3-251/2*x^2-3438*x+5670,-20*x^3-118*x^2+1190*x-17150,801/4*x^3+1531/4*x^2-14305*x-8711,29*x^3-496*x^2+677*x+25780,289*x^3+23*x^2-21192*x+13536,-1419/8*x^3-3217/8*x^2+18193/2*x+102525/2,-73/2*x^3-347/2*x^2+3646*x-9096,1463/8*x^3+5653/8*x^2-19749/2*x-44033/2,487/4*x^3-4915/4*x^2-6827*x+95447,993/4*x^3+1903/4*x^2-16332*x-60207,265*x^3-45*x^2-37636*x+26102]]];

f[18,6]=[
[x+96, [1,1], [-4,0,-96,-148,384,-334,576,-664,-3840,96,-4564,5798,-6720,-14872,-19200,7776,-13056,42782,36656,64512,-16810,28076,-66432,-81792,-29938]],
[x-66, [1,-1], [-4,0,66,176,60,-658,414,956,-600,-5574,-3592,-8458,-19194,13316,19680,31266,-26340,-31090,-16804,-6120,-25558,74408,6468,32742,166082]],
[x-4, [-1,1], [4,0,96,-148,-384,-334,-576,-664,3840,-96,-4564,5798,6720,-14872,19200,-7776,13056,42782,36656,-64512,-16810,28076,66432,81792,-29938]]];

f[19,6]=[
[x+2, [1], [-2,-1,-24,-167,262,749,-1597,-361,-2011,-1055,-1548,9378,-10248,10544,-6912,-35291,33655,-26218,45083,30942,46969,-64430,-13986,-137700,-22162]],
[x+6, [-1], [-6,4,54,248,204,-370,1554,361,-408,6174,-7840,-5146,-7830,-12532,2592,-20778,18972,-18418,-11548,-72984,59114,-44752,-27660,20730,14018]],
[x^2+7*x-32, [1], [x,-3*x-14,5*x-49,14*x+85,13*x-307,-29*x-772,-42*x+1245,-361,-273*x-2312,-179*x-4514,884*x+6660,-924*x-6358,-1138*x-6070,1139*x+16665,9*x+5895,1299*x-10020,89*x-31946,3975*x-6557,1967*x+16404,-5632*x-54830,-3584*x+20985,1998*x-9432,-3722*x+22740,-9436*x-76660,1798*x-24936]],
[x^4-9*x^3-72*x^2+774*x-1140, [-1], [x,3/22*x^3-15/22*x^2-105/11*x+543/11,-23/22*x^3+27/22*x^2+893/11*x-1512/11,9/11*x^3-23/11*x^2-630/11*x+1399/11,107/22*x^3+81/22*x^2-4185/11*x+1998/11,-153/22*x^3+369/22*x^2+6147/11*x-17639/11,-109/11*x^3+369/11*x^2+7982/11*x-29943/11,361,541/22*x^3-549/22*x^2-22367/11*x+69255/11,889/22*x^3-2025/22*x^2-33755/11*x+105381/11,450/11*x^3+346/11*x^2-33876/11*x+54616/11,306/11*x^3-2630/11*x^2-36468/11*x+206362/11,-1197/11*x^3+441/11*x^2+96374/11*x-110376/11,-4347/22*x^3+8799/22*x^2+171945/11*x-406856/11,-1293/22*x^3-5679/22*x^2+48511/11*x+184572/11,4487/22*x^3+1809/22*x^2-169541/11*x+229257/11,3015/22*x^3-5571/22*x^2-161581/11*x+414639/11,-5733/22*x^3+6225/22*x^2+220455/11*x-524006/11,8289/22*x^3+4491/22*x^2-361395/11*x+314971/11,-3668/11*x^3+6768/11*x^2+313256/11*x-675054/11,-1008/11*x^3+1344/11*x^2+106992/11*x-466877/11,3537/11*x^3+5679/11*x^2-314910/11*x-377042/11,-2843/11*x^3+1323/11*x^2+287538/11*x-874638/11,-10*x^3-1098*x^2-2668*x+61992,-9729/11*x^3+6581/11*x^2+779238/11*x-406742/11]]];

f[20,6]=[
[x, [-1,1], [0,22,-25,218,-480,-622,186,-1204,-3186,5526,9356,5618,-14394,-370,16146,-4374,-11748,13202,-11542,-29532,33698,31208,-38466,119514,94658]]];

f[21,6]=[
[x-1, [1,1], [1,-9,-34,-49,-340,454,-798,892,-3192,-8242,-2496,9798,19834,-17236,8928,150,-42396,14758,-1676,14568,78378,-2272,-37764,-117286,10002]],
[x+6, [1,-1], [-6,-9,78,49,444,-442,-126,2684,4200,-5442,80,-5434,7962,-11524,-13920,-9594,27492,49478,-59356,32040,-61846,-65776,40188,-7974,-143662]],
[x-5, [-1,1], [5,9,94,-49,52,-770,-2022,1732,-576,5518,6336,-7338,-3262,5420,864,4182,-11220,-45602,1396,18720,46362,97424,-81228,-3182,4914]],
[x-10, [-1,1], [10,9,-106,-49,92,670,-222,-908,-1176,1118,3696,4182,-6662,-3700,-7056,-37578,32700,-10802,64996,-61320,38922,-88096,71892,111818,-150846]]];

f[22,6]=[
[x-1, [1,1], [-4,1,-51,-166,-121,692,-738,1424,-1779,-2064,6245,-14785,5304,17798,-17184,-30726,-34989,-45940,25343,13311,-53260,77234,55014,125415,-88807]],
[x+21, [1,-1], [-4,-21,81,98,121,824,978,-2140,3699,3480,-7813,-13597,6492,14234,-20352,-366,9825,26132,17093,-23583,-35176,-42490,22674,-17145,-30727]],
[x+29, [-1,-1], [4,-29,-31,-230,121,112,-1142,-612,-1941,1192,-1037,8083,-10444,58,8656,-20318,-21351,47044,48093,-24967,-42288,-72410,-15806,-114761,-5159]],
[x^2-29*x+12, [-1,1], [4,x,-5*x+66,-6*x+80,-121,-10*x-178,124*x-1902,-44*x-436,-7*x+276,-366*x+7518,89*x+5900,149*x-4294,1014*x-19758,-470*x+1916,-312*x+15096,388*x+14166,-333*x+50304,526*x-22402,1495*x-53752,-4173*x+72300,-2926*x+22898,3258*x-74728,-5278*x+91524,1001*x-23538,-8213*x+103934]]];

f[23,6]=[
[x^3+4*x^2-48*x-8, [1], [x,-1/4*x^2-7/2*x-2,1/2*x^2-38,-x^2+11*x-42,7*x^2+45*x-156,-99/4*x^2-207/2*x+414,-73/2*x^2-276*x+696,50*x^2+340*x-862,-529,523/4*x^2+79/2*x-5110,479/4*x^2-391/2*x-5738,831/2*x^2+1376*x-10698,-1847/4*x^2-3199/2*x+10842,-575/2*x^2+325*x+5590,-1021/4*x^2-4427/2*x+14078,267/2*x^2+5245*x+7712,495*x^2+3904*x+4784,-21/2*x^2+1259*x-21704,-359*x^2-6477*x-16220,2227/4*x^2+3425/2*x+14298,-21/4*x^2+6419/2*x-22782,-3331/2*x^2-14771*x+61892,-6879/2*x^2-14770*x+112012,4333/2*x^2+7035*x-62322,309/2*x^2+4278*x-91288]],
[x^6-4*x^5-144*x^4+381*x^3+5928*x^2-7784*x-77528, [-1], [x,-9/412*x^5+71/618*x^4+748/309*x^3-4161/412*x^2-29389/618*x+49832/309,15/206*x^5-28/103*x^4-854/103*x^3+3639/206*x^2+18330/103*x-9408/103,-1/206*x^5+98/103*x^4-204/103*x^3-22573/206*x^2+11962/103*x+252318/103,-9/103*x^5+13/103*x^4+1066/103*x^3-865/103*x^2-23129/103*x+13226/103,5/412*x^5-799/206*x^4+1128/103*x^3+186613/412*x^2-137163/206*x-1035276/103,87/103*x^5-469/103*x^4-10236/103*x^3+42901/103*x^2+227975/103*x-695244/103,-123/206*x^5-409/103*x^4+9310/103*x^3+119881/206*x^2-289047/103*x-1570360/103,529,1663/412*x^5-5693/206*x^4-44820/103*x^3+1067423/412*x^2+1830615/206*x-4424640/103,-1377/412*x^5+11037/206*x^4+27848/103*x^3-2348905/412*x^2-383143/206*x+12104364/103,1331/206*x^5-2718/103*x^4-74350/103*x^3+423923/206*x^2+1475072/103*x-2252660/103,-83/412*x^5+9885/206*x^4-10732/103*x^3-2205219/412*x^2+1381465/206*x+11245036/103,-895/103*x^5+6500/103*x^4+94426/103*x^3-641281/103*x^2-1740154/103*x+11773300/103,5083/412*x^5-25055/206*x^4-121576/103*x^3+4946739/412*x^2+3577613/206*x-23356116/103,952/103*x^5-5312/103*x^4-114430/103*x^3+500362/103*x^2+2596754/103*x-7970394/103,-248/103*x^5+9262/103*x^4+7584/103*x^3-1095356/103*x^2+396078/103*x+24360520/103,3020/103*x^5-16150/103*x^4-344770/103*x^3+1409774/103*x^2+7655272/103*x-20833758/103,-1265/103*x^5-17697/103*x^4+201790/103*x^3+2322495/103*x^2-6369635/103*x-55960314/103,-1881/412*x^5-5903/206*x^4+72024/103*x^3+1856143/412*x^2-4798083/206*x-15962136/103,-19337/412*x^5+29799/206*x^4+576876/103*x^3-3821177/412*x^2-26590549/206*x+6655880/103,12069/206*x^5-20407/103*x^4-707028/103*x^3+2545933/206*x^2+15880185/103*x-3916308/103,-5613/206*x^5-5096/103*x^4+359366/103*x^3+2362931/206*x^2-9560158/103*x-39521702/103,3299/206*x^5+41833/103*x^4-330224/103*x^3-9858597/206*x^2+11522053/103*x+109427502/103,5942/103*x^5-40387/103*x^4-645476/103*x^3+3736740/103*x^2+13516041/103*x-58432300/103]]];

f[24,6]=[
[x+34, [1,1], [0,-9,-34,-240,-124,46,1954,-1924,2840,-8922,-4648,-4362,-2886,11332,7008,-22594,-28,-6386,-39076,-54872,21034,26632,56188,64410,-116158]],
[x-9, [1,-1], [0,9,38,120,524,-962,-1358,-2284,2552,3966,-2992,13206,-15126,-7316,-6960,-17482,33884,39118,32996,14248,-35990,-29888,-51884,30714,-48478]],
[x-94, [-1,1], [0,-9,94,144,-380,814,-862,-1156,-488,-5466,9560,-10506,-5190,-17084,3168,-24770,17380,4366,-5284,8360,39466,42376,-61828,-63078,-16318]]];

f[25,6]=[
[x+2, [1], [-2,4,0,-192,-148,-286,1678,1060,-2976,-3410,-2448,-182,-9398,1244,12088,-23846,-20020,32302,-60972,-32648,38774,-33360,-16716,101370,119038]],
[x^2+5*x-54, [1], [x,-2*x-15,0,-4*x-110,50*x+27,-32*x+100,136*x-405,-70*x-1765,-12*x-810,-80*x-2160,-1100*x-3298,-384*x-1970,400*x+14877,2128*x+6820,-1544*x-16740,-752*x+11610,-1960*x+1080,2000*x-7198,1586*x+23995,1000*x-41148,-1112*x+32365,5020*x+45290,858*x-44145,-10440*x-62505,-10944*x+35710]],
[x^2-44, [-1], [x,3*x,0,-9*x,252,18*x,-104*x,220,-367*x,6930,6752,2106*x,-198,63*x,-1589*x,878*x,24660,-5698,-6579*x,53352,-10692*x,-51920,9323*x,9990,-15264*x]],
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f[26,6]=[
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f[27,6]=[
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f[28,6]=[
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f[29,6]=[
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f[30,6]=[
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f[31,6]=[
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f[51,6]=[
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f[56,6]=[
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f[57,6]=[
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f[58,6]=[
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f[69,6]=[
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f[70,6]=[
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