eigenvalues | | standard Euler factors | | spinor Euler factors | | identified eigenforms | | special values |
[a b c d e f] | = |
|
t1 | ½ [0 0 0 0 0 0] |
t2 | ½ [2 0 0 0 0 0] |
t3 | ½ [2 2 0 1 0 0] |
t4 | ½ [2 2 2 1 1 1] |
t1 | t2 | t3 | t4 | |
t1 | 411162568697368361/6857444385792000 | 595025425032371/104661849600 | 14147393381239/568814400 | 237449482847/5745600 |
t2 | 595025425032371/104661849600 | 11864814481613/20766240 | 314046090217/112860 | 6067815041/1140 |
t3 | 14147393381239/568814400 | 314046090217/112860 | 457379889638/28215 | 10963328374/285 |
t4 | 237449482847/5745600 | 6067815041/1140 | 10963328374/285 | 11130020166/95 |
u1 | ½ [0 0 0 0 0 0] |
u2 | ½ [2 0 0 0 0 0] |
u3 | ½ [4 0 0 0 0 0] |
u4 | ½ [2 2 0 1 0 0] |
u5 | ½ [4 4 0 2 0 0] |
u6 | ½ [2 2 2 1 1 1] |
u7 | ½ [2 2 2 0 0 0] |
u8 | ½ [2 2 4 0 0 0] |
u9 | ½ [2 2 6 1 1 1] |
u10 | ½ [4 4 4 2 2 2] |
u11 | ½ [2 6 6 0 0 2] |
u12 | ½ [4 4 4 0 0 0] |
u13 | ½ [8 8 8 4 4 4] |
g1 | g2 | g3 | g4 | |
f1 | 1 | 0 | 0 | 0 |
f2 | -65520 | 691 | 0 | 0 |
f3 | 452088000 | -7146836 | 543781 | 0 |
f4 | -89513424000 | 1650869528 | -197834263 | 21826375 |
f | λ2(f) | λ0,4(f) | λ1,4(f) | λ2,4(f) | λ3,4(f) |
f1 | 1077415425 | 1154901456286648065 | 1971774054270720 | 481154236416 | 16777216 |
f2 | -12619800 | -685867303258560 | 280677902238720 | 206045577216 | 16777216 |
f3 | 1428192 | 731393197056 | 91455307776 | 68780556288 | 16777216 |
f4 | -47808 | -1676242944 | 235339776 | 66060288 | 16777216 |
u | a(u; f1) | a(u; f2) | a(u; f3) | a(u; f4) |
u1 | 411162568697368361/6857444385792000 | 0 | 0 | 0 |
u2 | 595025425032371/104661849600 | 107235250318/4807 | 0 | 0 |
u3 | 406402365297109393/34887283200 | -2573646007632/4807 | 0 | 0 |
u4 | 14147393381239/568814400 | 61277285896/209 | 1895054400000/11 | 0 |
u5 | 396169456854835717/7584192 | -1507421233041600/209 | 5275831449600000/11 | 0 |
u6 | 237449482847/5745600 | 18433615272/19 | 1561524825600 | 34538279731200 |
u7 | 9735428796727/229824 | 9273396066000/19 | 422854858598400 | 5664277875916800 |
u8 | 11867962602175907/273600 | 6368840643033072/19 | 144466455257395200 | -34814585969049600 |
u9 | 248984066375258719/5745600 | 9718117528827144/19 | 301858045667596800 | 45866835483033600 |
u10 | 10228284879561304375/229824 | -237376516795377600/19 | 2013655576120934400 | -4551316349858611200 |
u11 | 13754430212387729078789/302400 | 3395356035305291568816/19 | 202348537429166899200 | 60539801937798758400 |
u12 | 261844591370961233905247/5745600 | -126820607424689324928/19 | 381198762208242892800 | -235430598247081574400 |
u13 | 54913000017403178146901052947/1149120 | -7400374905526772072547840/19 | 1197153345953967833088000 | 73635214505935896576000 |
f | Q2(f, x, st)/(1-x) |
f1 | (1-2048*x)*(1-1024*x)*(1-512*x)*(1-x/512)*(1-x/1024)*(1-x/2048) |
f2 | (1-1024*x)*(1-512*x)*(1-x/512)*(1-x/1024)*(1+(55*x)/32+x^2) |
f3 | (1-512*x)*(1-x/512)*(1+(9*x)/64+x^2/2)*(1+(9*x)/32+2*x^2) |
f4 | (1-(57*x)/128+x^2/2)*(1+(55*x)/32+x^2)*(1-(57*x)/64+2*x^2) |
f | Q2(f, x, spin) |
f1 | (1-1073741824*x)*(1-2097152*x)*(1-1048576*x)*(1-524288*x)*(1-2048*x)*(1-1024*x)*(1-512*x)*(1-x) |
f2 | (1+24*x+2048*x^2)*(1+12288*x+536870912*x^2)*(1+24576*x+2147483648*x^2)*(1+12582912*x+562949953421312*x^2) |
f3 | (1-1048576*x)*(1-524288*x)*(1-2048*x)*(1-1024*x)*(1+288*x+2097152*x^2)*(1+147456*x+549755813888*x^2) |
f4 | (1+12288*x+536870912*x^2)*(1+24576*x+2147483648*x^2)*(1+10944*x-1419640832*x^2+11751030521856*x^3+1152921504606846976*x^4) |
c1 | 2^13*3^7*5^3*7^2*11*13*19*23/(131*283*593*617*691*43867) |
c2 | 11*19*23/(2*7*283*617*691*43867) |
c3 | 11/(2^9*3^3*5^5*7*131*593*43867) |
c4 | 1/(2^16*3^11*5^5*7*17*283*617) |
2u | det(2u) | a(u; f4) |
[2 2 2 1 1 1] | 4 | 34538279731200 |
[2 2 2 1 0 0] | 6 | 621689035161600 |
[2 2 2 0 0 0] | 8 | 5664277875916800 |
[2 2 4 1 1 1] | 10 | -3661057651507200 |
[2 2 4 0 1 1] | 12 | -14091618130329600 |
[2 2 4 1 0 0] | 12 | -1865067105484800 |
[2 2 4 0 1 0] | 14 | -33847514136576000 |
[2 2 4 0 0 0] | 16 | -34814585969049600 |
[2 2 6 1 1 1] | 16 | 45866835483033600 |
[2 2 6 1 0 0] | 18 | -33571207898726400 |
[2 2 6 0 1 1] | 20 | 362306554380288000 |
[2 4 4 1 1 2] | 20 | 211926884430643200 |
[2 2 6 0 1 0] | 22 | 223738976098713600 |
[2 2 8 1 1 1] | 22 | -240455503488614400 |
[2 2 6 0 0 0] | 24 | 129311319313612800 |
[2 4 4 0 0 2] | 24 | 1086712433462476800 |
[2 2 8 1 0 0] | 24 | 188993466689126400 |
[2 4 4 1 1 1] | 24 | 69629171938099200 |
[2 4 4 1 0 1] | 26 | -1093274706611404800 |
[2 2 8 0 1 1] | 28 | -2533728201080832000 |
[2 4 4 1 0 0] | 28 | 2572411074379776000 |
[2 2 10 1 1 1] | 28 | 595232712887500800 |
[2 4 4 0 0 1] | 30 | -2587469764342579200 |
[2 2 8 0 1 0] | 30 | -905593694552064000 |
[2 2 10 1 0 0] | 30 | 197697113181388800 |
[2 2 8 0 0 0] | 32 | -369145133767065600 |
[2 4 4 0 0 0] | 32 | 4272799662106214400 |
[4 4 4 2 2 2] | 32 | -4551316349858611200 |
[2 2 12 1 1 1] | 34 | -441813674321510400 |
[2 4 6 1 1 2] | 34 | 1414964244027801600 |
[2 2 10 0 1 1] | 36 | 6515611933011148800 |
[2 4 6 0 1 2] | 36 | 2239013060134502400 |
[2 2 12 1 0 0] | 36 | -3978188135999078400 |
[4 4 4 2 2 1] | 36 | 4938697695323750400 |
[2 2 10 0 1 0] | 38 | 4656658103038771200 |
[2 4 6 1 1 1] | 38 | -4163037009120460800 |
[2 2 10 0 0 0] | 40 | 1381531189248000 |
[2 4 6 0 0 2] | 40 | 2333129872402022400 |
[2 4 6 1 0 1] | 40 | -3504668320884326400 |
[2 2 14 1 1 1] | 40 | -1112961526058188800 |
[2 4 6 0 1 1] | 42 | -957401114148864000 |
[2 2 14 1 0 0] | 42 | 10714188831975014400 |
[2 4 6 1 0 0] | 42 | -426478678120857600 |
[2 2 12 0 1 1] | 44 | 1530460251448934400 |
[2 4 6 0 1 0] | 44 | -11998529302059417600 |
[4 4 4 2 1 1] | 44 | -8681818299472281600 |
[2 4 6 0 0 1] | 46 | 1564031459347660800 |
[2 2 12 0 1 0] | 46 | -17003747724145459200 |
[2 2 16 1 1 1] | 46 | 3420809377696972800 |
[2 2 12 0 0 0] | 48 | -1498685034096230400 |
[2 4 6 0 0 0] | 48 | -9260679867767193600 |
[2 2 16 1 0 0] | 48 | -2476809116083814400 |
[2 4 8 1 1 2] | 48 | 3567666143114035200 |
[2 6 6 1 1 3] | 48 | 8663858394012057600 |
[4 4 4 2 0 0] | 48 | -8076983944819507200 |
[4 4 4 1 1 -1] | 50 | 12656897990295552000 |
[2 2 14 0 1 1] | 52 | -44387699115265228800 |
[2 4 8 0 1 2] | 52 | -13927768531284787200 |
[2 2 18 1 1 1] | 52 | -5859557309517004800 |
[2 4 8 1 1 1] | 52 | 21815206396939468800 |
[2 6 6 0 0 3] | 54 | -9830768713010380800 |
[2 2 14 0 1 0] | 54 | 20303120510307532800 |
[2 2 18 1 0 0] | 54 | -34897270610726092800 |
[2 4 8 1 0 1] | 54 | 32836371459165388800 |
[4 4 4 1 1 1] | 54 | 65368736980136755200 |
[2 2 14 0 0 0] | 56 | 32570979317710848000 |
[2 4 8 0 0 2] | 56 | -26845914069467136000 |
[2 4 8 1 0 0] | 56 | -47115739678113792000 |
[2 6 6 1 1 2] | 56 | -6576088460820480000 |
[4 4 4 1 1 0] | 56 | 16014709545762816000 |
[4 4 6 2 2 2] | 56 | -54173429911506124800 |
[2 4 8 0 1 1] | 58 | 81152316357938380800 |
[2 6 6 1 0 2] | 58 | -10758190600352563200 |
[2 2 20 1 1 1] | 58 | 4096032746441932800 |
[2 2 16 0 1 1] | 60 | 89846499361554432000 |
[2 4 8 0 1 0] | 60 | -64362222432210124800 |
[2 2 20 1 0 0] | 60 | 47447307163533312000 |
[2 6 6 1 1 1] | 60 | 51457201440325632000 |
[4 4 4 1 0 0] | 60 | -17382425423118336000 |
[4 4 6 2 2 1] | 60 | 179339879351137075200 |
[2 4 8 0 0 1] | 62 | 43832668959984844800 |
[2 2 16 0 1 0] | 62 | 47546224796683468800 |
[2 4 10 1 1 2] | 62 | -89855341161165619200 |
[2 2 16 0 0 0] | 64 | -99160782639464448000 |
[2 4 8 0 0 0] | 64 | -19319332150444032000 |
[2 6 6 0 0 2] | 64 | 60539801937798758400 |
[2 6 6 1 0 1] | 64 | -45862414583228006400 |
[2 2 22 1 1 1] | 64 | 24695146314045849600 |
[4 4 4 0 0 0] | 64 | -235430598247081574400 |
[4 4 6 0 2 2] | 64 | 171928793439535104000 |
[2 2 22 1 0 0] | 66 | 12984597188385177600 |
[2 6 6 1 0 0] | 66 | 157813274819631513600 |
[2 4 10 1 1 1] | 66 | -14513123296169164800 |
[4 4 6 1 2 2] | 66 | -142984747952957030400 |
[2 2 18 0 1 1] | 68 | -15759333505430323200 |
[2 4 10 0 1 2] | 68 | -181940957197693747200 |
[2 4 10 1 0 1] | 68 | 12025952696165990400 |
[4 4 6 2 1 1] | 68 | -117484307108698521600 |
[2 6 6 0 0 1] | 70 | -81198252269980876800 |
[2 2 18 0 1 0] | 70 | -161955519784353792000 |
[2 4 10 1 0 0] | 70 | 40420701381899059200 |
[2 2 24 1 1 1] | 70 | -63094667566075084800 |
[2 6 8 1 1 3] | 70 | -62617901152665600000 |