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 | 12080581424652674443/20832215040 | 0 | 0 |
u2 | 11218859197184483/1192320 | 112491331633296000 | 0 |
u3 | 125526772203391842130081/397440 | 1376893899191543040000 | 0 |
u4 | -18361471681153/8832 | -94974591714710400 | -396362502144000 |
u5 | -75226949477683841/8832 | 17898982533165888000 | -7927250042880000 |
u6 | -102709867807354897963/2944 | 24451529733772038374400 | 133177800720384000 |
u7 | -308054394834058691201/8832 | -416979395062743293827200 | 91956100497408000 |
u8 | -1262715114805259643875969/8832 | -2418597082530849040128000 | 132670456717639680000 |
u9 | -5169557528790298430001336961/8832 | -1689325359518984403257395200 | -2994395038597251072000 |
u10 | -5172081726501531983973675649/8832 | 299468692111551860833689600 | 4835394221355565056000 |
u11 | -86773152975921590746522484699787905/8832 | -27130025762780132634389950464000 | 8719725433918649794560000 |
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 | 1-68778211329*x+4037196501611460608*x^2-67762439453475524157898752*x^3+325489471123543815207609207619584*x^4-4656599381597719836714129278707433472*x^5+19065121443968549176659183324806846087168*x^6-22319805663700699496353649140772407527604224*x^7+22300745198530623141535718272648361505980416*x^8 |
f2 | 1-25079760*x+279307968512000*x^2-3531356445139733053440*x^3+19850241180948448496591044608*x^4-242672967078303545835120324771840*x^5+1318994588899479052747613879140352000*x^6-8138847441300464285307125038607562178560*x^7+22300745198530623141535718272648361505980416*x^8 |
f3 | 1+293760*x+72679424000*x^2-14864280516034560*x^3-13175261569573969723392*x^4-1021465579119015020891996160*x^5+343218875891871681215782191104000*x^6+95330570322699435259819912604480962560*x^7+22300745198530623141535718272648361505980416*x^8 |
c1 | -20832215040/12080581424652674443 |
c2 | -1/74011534312826070576000 |
c3 | 1/1369432444907520000 |