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 2 0 1 0 0] |
t3 | ½ [2 2 2 1 1 1] |
t1 | t2 | t3 | |
t1 | -103*131*593*657931*2294797/(2^13*3^5*5*7*13*23) | -13*47*103*131*593*2294797/(2^7*3^4*5*23) | 103*131*593*2294797/(2^7*3*23) |
t2 | -13*47*103*131*593*2294797/(2^7*3^4*5*23) | -7*59*131*593*62645567/(2*3^3*5*23) | 7*131*593*1867*8069/(2*23) |
t3 | 103*131*593*2294797/(2^7*3*23) | 7*131*593*1867*8069/(2*23) | -3^3*5*7*11^2*307*19141/(2*23) |
u1 | ½ [0 0 0 0 0 0] |
u2 | ½ [2 2 0 1 0 0] |
u3 | ½ [4 4 0 2 0 0] |
u4 | ½ [2 2 2 1 1 1] |
u5 | ½ [2 2 2 0 0 0] |
u6 | ½ [2 2 4 0 0 0] |
u7 | ½ [2 2 6 1 1 1] |
u8 | ½ [4 4 4 2 2 2] |
u9 | ½ [2 6 6 0 0 2] |
u10 | ½ [4 4 4 0 0 0] |
u11 | ½ [8 8 8 4 4 4] |
g1 | g2 | g3 | |
f1 | -1 | 0 | 0 |
f2 | 10675392 | -657931 | 0 |
f3 | 34944 | -2917 | -3455 |
f | λ2(f) | λ0,4(f) | λ1,4(f) | λ2,4(f) | λ3,4(f) |
f1 | 68778211329 | 4724386558799742245889 | 2017982459832966144 | 123152825843712 | 1073741824 |
f2 | 25079760 | 209967984380160 | 51629363527680 | 17599555436544 | 1073741824 |
f3 | -293760 | -87148707840 | 46489927680 | -7398752256 | 1073741824 |
u | a(u; f1) | a(u; f2) | a(u; f3) |
u1 | 103*131*593*657931*2294797/(2^13*3^5*5*7*13*23) | 0 | 0 |
u2 | 13*47*103*131*593*2294797/(2^7*3^4*5*23) | 2^7*3^5*5^3*7^2*11*131*593*691 | 0 |
u3 | 13*17*47*103*131*241*593*2731*2294797/(2^7*3^3*5*23) | 2^11*3^7*5^4*7^2*11*17*131*593*691 | 0 |
u4 | -103*131*593*2294797/(2^7*3*23) | -2^7*3^5*5^2*7^2*11*131*593*2917 | -2^15*3^8*5^3*7^3*43 |
u5 | -17*103*131*241*593*2294797/(2^7*3*23) | 2^9*3^5*5^3*7^2*11*131*593*27487 | -2^17*3^8*5^4*7^3*43 |
u6 | -19*37*73*103*109*131*593*2294797/(2^7*23) | 2^10*3^6*5^2*7^2*11*131*593*31291313 | 2^19*3^9*5^3*7^4*43 |
u7 | -97*103*131*257*593*673*2294797/(2^7*3*23) | -2^7*3^5*5^2*7^3*11*131*433*593*4225301 | 2^18*3^8*5^3*7^3*29*43 |
u8 | -17^3*103*131*241^3*593*2294797/(2^7*3*23) | -2^11*3^5*5^3*7^2*11*131*593*27061*34313 | 2^22*3^8*5^4*7^3*43*523 |
u9 | -7*103*131*593*2294797*40220535217591/(2^7*3*23) | -2^11*3^5*5^2*7^2*11*31*131*593*241441*433261 | -2^22*3^8*5^3*7^3*43*59021 |
u10 | -13*103*131*593*10069*10429*206341*2294797/(2^7*3*23) | 2^13*3^5*5^2*7^3*11*131*331*593*811*76481 | 2^24*3^8*5^3*7^3*43*23827 |
u11 | -5*7*103*131*593*1901*2027*2294797*35040797444293/(2^7*3*23) | -2^15*3^5*5^3*7^2*11*131*593*650982374940649 | 2^29*3^8*5^4*7^3*43*268547 |
f | Q2(f, x, st)/(1-x) |
f1 | 1-(117440519*x)/8192+(1970325248016391*x^2)/33554432-(4722369930938315440129*x^3)/68719476736+(1970325248016391*x^4)/33554432-(117440519*x^5)/8192+x^6 |
f2 | 1-(4194269*x)/2048-(34078657*x^2)/1048576-(1374418173961*x^3)/268435456-(34078657*x^4)/1048576-(4194269*x^5)/2048+x^6 |
f3 | 1+(889*x)/512+(462721*x^2)/131072+(18170351*x^3)/4194304+(462721*x^4)/131072+(889*x^5)/512+x^6 |
f | Q2(f, x, spin) |
f1 | (1-68719476736*x)*(1-33554432*x)*(1-16777216*x)*(1-8388608*x)*(1-8192*x)*(1-4096*x)*(1-2048*x)*(1-x) |
f2 | (1-16777216*x)*(1-8388608*x)*(1-8192*x)*(1-4096*x)*(1+48*x+33554432*x^2)*(1+98304*x+140737488355328*x^2) |
f3 | (1+98304*x+34359738368*x^2)*(1+196608*x+137438953472*x^2)*(1-1152*x-118106882048*x^2-79164837199872*x^3+4722366482869645213696*x^4) |
c1 | -20832215040/12080581424652674443 |
c2 | -1/74011534312826070576000 |
c3 | 1/1369432444907520000 |