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 | 1-1077415425*x+3948360489766400*x^2-4147368577200016588800*x^3+1252772137538465207836213248*x^4-4453203100883030624888369971200*x^5+4552149716591705120038218786406400*x^6-1333775693551174685167056757928755200*x^7+1329227995784915872903807060280344576*x^8 |
f2 | 1+12619800*x+563417099110400*x^2+20803725603687628800*x^3+1682161801676480732725248*x^4+22337830275699055673946931200*x^5+649575689627587392863438530150400*x^6+15622555707773641993171967882035200*x^7+1329227995784915872903807060280344576*x^8 |
f3 | 1-1428192*x+871555039232*x^2-786046410653958144*x^3+304415950273588582416384*x^4-844010906724234050358214656*x^5+1004834547179036984903500562432*x^6-1768016060587065825568730023723008*x^7+1329227995784915872903807060280344576*x^8 |
f4 | 1+47808*x+1970143232*x^2+31682363129856*x^3-1067313529268207616*x^4+34018678375681930297344*x^5+2271420499328436390626066432*x^6+59183437398155460182377330900992*x^7+1329227995784915872903807060280344576*x^8 |
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) |