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 | -12080581424652674443/20832215040 | -11218859197184483/1192320 | 18361471681153/8832 |
t2 | -11218859197184483/1192320 | -2009862675060793/6210 | 8191964515763/46 |
t3 | 18361471681153/8832 | 8191964515763/46 | -671924037015/46 |
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 | (1-8192*x)*(1-4096*x)*(1-2048*x)*(1-x/2048)*(1-x/4096)*(1-x/8192) |
f2 | (1-2048*x)*(1-x/2048)*(1+(3*x)/512+x^2/2)*(1+(3*x)/256+2*x^2) |
f3 | (1+(3*x)/512+x^2/2)*(1+(55*x)/32+x^2)*(1+(3*x)/256+2*x^2) |
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 |
2u | det(2u) | a(u; f3) |
[2 2 2 1 1 1] | 4 | -396362502144000 |
[2 2 2 1 0 0] | 6 | 2378175012864000 |
[2 2 2 0 0 0] | 8 | -7927250042880000 |
[2 2 4 1 1 1] | 10 | -91163375493120000 |
[2 2 4 0 1 1] | 12 | 380508002058240000 |
[2 2 4 1 0 0] | 12 | 535089377894400000 |
[2 2 4 0 1 0] | 14 | -410631552221184000 |
[2 2 4 0 0 0] | 16 | 133177800720384000 |
[2 2 6 1 1 1] | 16 | 91956100497408000 |
[2 2 6 1 0 0] | 18 | -3210536267366400000 |
[2 2 6 0 1 1] | 20 | 3975515896504320000 |
[2 4 4 1 1 2] | 20 | 6500345035161600000 |
[2 2 6 0 1 0] | 22 | -9635572427120640000 |
[2 2 8 1 1 1] | 22 | 5013985652121600000 |
[2 2 6 0 0 0] | 24 | 25417934537490432000 |
[2 4 4 0 0 2] | 24 | -41237554723061760000 |
[2 2 8 1 0 0] | 24 | -10292741455675392000 |
[2 4 4 1 1 1] | 24 | -26768737944797184000 |
[2 4 4 1 0 1] | 26 | 30125928337956864000 |
[2 2 8 0 1 1] | 28 | -8878520048025600000 |
[2 4 4 1 0 0] | 28 | 5771038031216640000 |
[2 2 10 1 1 1] | 28 | -15953590711296000000 |
[2 4 4 0 0 1] | 30 | -76696144164864000000 |
[2 2 8 0 1 0] | 30 | 29418024909127680000 |
[2 2 10 1 0 0] | 30 | 123070556915712000000 |
[2 2 8 0 0 0] | 32 | -108698452587970560000 |
[2 4 4 0 0 0] | 32 | 80414024434974720000 |
[4 4 4 2 2 2] | 32 | 132670456717639680000 |
[2 2 12 1 1 1] | 34 | -64106085646761984000 |
[2 4 6 1 1 2] | 34 | -186629662309515264000 |
[2 2 10 0 1 1] | 36 | -22520128284315648000 |
[2 4 6 0 1 2] | 36 | 331288102904500224000 |
[2 2 12 1 0 0] | 36 | -301084091153620992000 |
[4 4 4 2 2 1] | 36 | 329329675781406720000 |
[2 2 10 0 1 0] | 38 | 82867508323246080000 |
[2 4 6 1 1 1] | 38 | 297283767483064320000 |
[2 2 10 0 0 0] | 40 | -133574163222528000000 |
[2 4 6 0 0 2] | 40 | 37797128204451840000 |
[2 4 6 1 0 1] | 40 | 13983669075640320000 |
[2 2 14 1 1 1] | 40 | 394555089134223360000 |
[2 4 6 0 1 1] | 42 | -252704876866928640000 |
[2 2 14 1 0 0] | 42 | 95721544267776000000 |
[2 4 6 1 0 0] | 42 | -319793193979822080000 |
[2 2 12 0 1 1] | 44 | -291595965577297920000 |
[2 4 6 0 1 0] | 44 | -774952902416867328000 |
[4 4 4 2 1 1] | 44 | 30694312166031360000 |
[2 4 6 0 0 1] | 46 | 425533196851789824000 |
[2 2 12 0 1 0] | 46 | 180486043526283264000 |
[2 2 16 1 1 1] | 46 | -464094511960375296000 |
[2 2 12 0 0 0] | 48 | 782324452231741440000 |
[2 4 6 0 0 0] | 48 | 651239445522677760000 |
[2 2 16 1 0 0] | 48 | -124140735671500800000 |
[2 4 8 1 1 2] | 48 | 359199553942978560000 |
[2 6 6 1 1 3] | 48 | -955170212166696960000 |
[4 4 4 2 0 0] | 48 | -3036453856424755200000 |
[4 4 4 1 1 -1] | 50 | 2818811206497484800000 |
[2 2 14 0 1 1] | 52 | 946684090995793920000 |
[2 4 8 0 1 2] | 52 | -3262634154648207360000 |
[2 2 18 1 1 1] | 52 | -508949270878003200000 |
[2 4 8 1 1 1] | 52 | 4217297022812160000 |
[2 6 6 0 0 3] | 54 | 4197048448027631616000 |
[2 2 14 0 1 0] | 54 | -2500465528375492608000 |
[2 2 18 1 0 0] | 54 | 3070364253933182976000 |
[2 4 8 1 0 1] | 54 | 1227181113788055552000 |
[4 4 4 1 1 1] | 54 | -5080117150154317824000 |
[2 2 14 0 0 0] | 56 | 1748003027055280128000 |
[2 4 8 0 0 2] | 56 | 4965578692459757568000 |
[2 4 8 1 0 0] | 56 | -3730842909380837376000 |
[2 6 6 1 1 2] | 56 | -5851211067250311168000 |
[4 4 4 1 1 0] | 56 | 189911543827267584000 |
[4 4 6 2 2 2] | 56 | -8497520556464701440000 |
[2 4 8 0 1 1] | 58 | 1044252684523560960000 |
[2 6 6 1 0 2] | 58 | 4296454578115338240000 |
[2 2 20 1 1 1] | 58 | -519254695933747200000 |
[2 2 16 0 1 1] | 60 | 2149870211629056000000 |
[2 4 8 0 1 0] | 60 | 3410302968446976000000 |
[2 2 20 1 0 0] | 60 | -4607761650924257280000 |
[2 6 6 1 1 1] | 60 | 5480385408394444800000 |
[4 4 4 1 0 0] | 60 | 1490640098063155200000 |
[4 4 6 2 2 1] | 60 | -525101042840371200000 |
[2 4 8 0 0 1] | 62 | -5194536699098234880000 |
[2 2 16 0 1 0] | 62 | 2934636256874004480000 |
[2 4 10 1 1 2] | 62 | 303042914639216640000 |
[2 2 16 0 0 0] | 64 | -9474243376047980544000 |
[2 4 8 0 0 0] | 64 | -519368055609360384000 |
[2 6 6 0 0 2] | 64 | -2994395038597251072000 |
[2 6 6 1 0 1] | 64 | 2942163973514723328000 |
[2 2 22 1 1 1] | 64 | 6628525497454952448000 |
[4 4 4 0 0 0] | 64 | 4835394221355565056000 |
[4 4 6 0 2 2] | 64 | 17512906161930633216000 |
[2 2 22 1 0 0] | 66 | -6768880630364160000000 |
[2 6 6 1 0 0] | 66 | -7120470024265973760000 |
[2 4 10 1 1 1] | 66 | -7099228165051072512000 |
[4 4 6 1 2 2] | 66 | -7120470024265973760000 |
[2 2 18 0 1 1] | 68 | -5466302648693268480000 |
[2 4 10 0 1 2] | 68 | -2842699974501703680000 |
[2 4 10 1 0 1] | 68 | -3700630574017413120000 |
[4 4 6 2 1 1] | 68 | 7018850605966295040000 |
[2 6 6 0 0 1] | 70 | -10800997092174643200000 |
[2 2 18 0 1 0] | 70 | 4012092228202168320000 |
[2 4 10 1 0 0] | 70 | 29085754223580364800000 |
[2 2 24 1 1 1] | 70 | -3669325863598080000000 |
[2 6 8 1 1 3] | 70 | -2606844467600916480000 |