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 | 131*283*593*617*691*43867/(2^13*3^7*5^3*7^2*11*13*19*23) | 0 | 0 | 0 |
u2 | 131*283*593*617*43867/(2^9*3^5*5^2*7*11*19*23) | 2*7*283*617*43867/(11*19*23) | 0 | 0 |
u3 | 131*283*593*617*683*43867/(2^9*3^4*5^2*7*11*19*23) | -2^4*3*7*283*617*43867/(11*19*23) | 0 | 0 |
u4 | 283*617*1847*43867/(2^6*3^5*5^2*7*11*19) | 2^3*283*617*43867/(11*19) | 2^9*3^3*5^5*43867/(11) | 0 |
u5 | 41*283*617*683*1847*43867/(2^6*3^4*7*11*19) | -2^6*3*5^2*41*283*617*43867/(11*19) | 2^14*3^4*5^5*29*43867/(11) | 0 |
u6 | 31*283*617*43867/(2^6*3^3*5^2*7*19) | 2^3*3*17509*43867/(19) | 2^9*3^3*5^2*103*43867 | 2^16*3^11*5^2*7*17 |
u7 | 31*41*283*617*43867/(2^6*3^3*7*19) | 2^4*3*5^3*11*3203*43867/(19) | 2^11*3^3*5^2*19*367*43867 | 2^18*3^11*5^2*7*17*41 |
u8 | 31*151*283*331*617*43867/(2^6*3^2*5^2*19) | 2^4*3^2*257*43867*3923077/(19) | 2^12*3^4*5^2*23*61*283*43867 | -2^20*3^13*5^2*7^2*17 |
u9 | 17*31*283*617*43867*61681/(2^6*3^3*5^2*7*19) | 2^3*3*47*3463*43867*56713/(19) | 2^9*3^3*5^2*167*43867*119227 | 2^20*3^11*5^2*7*17*83 |
u10 | 5^4*31*41^3*283*617*43867/(2^6*3^3*7*19) | -2^6*3*5^2*563*43867*2002397/(19) | 2^14*3^3*5^2*19*43867*218459 | -2^22*3^11*5^2*7*17*29*71 |
u11 | 31*79*283*617*43867*733236853/(2^6*3^3*5^2*7) | 2^4*3*43867*1612523857771451/(19) | 2^14*3^3*5^2*43867*417098303 | 2^24*3^11*5^2*7*17*41*167 |
u12 | 31*283*617*25117*43867*43904053/(2^6*3^3*5^2*7*19) | -2^7*3*2557*43867*2944353443/(19) | 2^16*3^3*5^2*31*43867*6336773 | -2^24*3^11*5^2*7*17*26627 |
u13 | 13*31*283*617*43867*17789370917002177/(2^6*3^3*5*7*19) | -2^9*3*5*7*311*16649*43867*606049343/(19) | 2^19*3^3*5^3*7*4261*43867*517081 | 2^28*3^11*5^3*7*17*19*5479 |
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) |