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 | 131*283*593*617*691*43867/(2^13*3^7*5^3*7^2*11*13*19*23) | 131*283*593*617*43867/(2^9*3^5*5^2*7*11*19*23) | 283*617*1847*43867/(2^6*3^5*5^2*7*11*19) | 31*283*617*43867/(2^6*3^3*5^2*7*19) |
t2 | 131*283*593*617*43867/(2^9*3^5*5^2*7*11*19*23) | 283*617*1549*43867/(2^5*3^3*5*11*19*23) | 41*283*617*43867/(2^2*3^3*5*11*19) | 43867*138323/(2^2*3*5*19) |
t3 | 283*617*1847*43867/(2^6*3^5*5^2*7*11*19) | 41*283*617*43867/(2^2*3^3*5*11*19) | 2*7^3*15199*43867/(3^3*5*11*19) | 2*29*31*139*43867/(3*5*19) |
t4 | 31*283*617*43867/(2^6*3^3*5^2*7*19) | 43867*138323/(2^2*3*5*19) | 2*29*31*139*43867/(3*5*19) | 2*3*131*641*22091/(5*19) |
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 | 1-1077415425*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 | 6857444385792000/411162568697368361 |
c2 | 4807/74099557969738 |
c3 | 11/1030494576686400000 |
c4 | 1/753845445268070400000 |