eigenvalues | | standard Euler factors | | spinor Euler factors | | identified eigenforms | | special values | | congruences |
[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 0 0 0 0] |
t5 | ½ [2 2 2 1 1 1] |
t6 | ½ [2 2 2 1 0 0] |
t7 | ½ [2 2 2 0 0 0] |
t1 | t2 | t3 | t4 | t5 | t6 | t7 | |
t1 | 13912726954911229324966739363569/234258606489600 | 3846482431548584275633602257/14354081280 | 15450190691937513287077/751680 | 445016619031983484355717/334080 | 12190127397766275077/27840 | 1334576754702420920447/10440 | 1377484395947589083701/192 |
t2 | 3846482431548584275633602257/14354081280 | 28545440207637342132869777/14952168 | 198714032425664085997/783 | 4529479453951814168837/348 | 256885152733794797/29 | 167522879746699791736/87 | 89320031445718918505 |
t3 | 15450190691937513287077/751680 | 198714032425664085997/783 | 219200918201873871032/783 | 211752845084675720518/87 | 643995985149579832/29 | 166342461853204298816/87 | 21909311729885244280 |
t4 | 445016619031983484355717/334080 | 4529479453951814168837/348 | 211752845084675720518/87 | 6856833942269137505217/58 | 3701424146518329462/29 | 696358864975982344752/29 | 1028680202152781023230 |
t5 | 12190127397766275077/27840 | 256885152733794797/29 | 643995985149579832/29 | 3701424146518329462/29 | 648262571812073064/29 | 193115326121315136 | 1642272118573723560 |
t6 | 1334576754702420920447/10440 | 167522879746699791736/87 | 166342461853204298816/87 | 696358864975982344752/29 | 193115326121315136 | 550935271481450279424/29 | 270848912004871421760 |
t7 | 1377484395947589083701/192 | 89320031445718918505 | 21909311729885244280 | 1028680202152781023230 | 1642272118573723560 | 270848912004871421760 | 11128058082662642490600 |
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 0 0 0] |
u5 | ½ [2 2 0 1 0 0] |
u6 | ½ [4 4 0 0 0 0] |
u7 | ½ [4 4 0 2 0 0] |
u8 | ½ [2 2 2 1 1 1] |
u9 | ½ [2 2 2 1 0 0] |
u10 | ½ [2 2 2 0 0 0] |
u11 | ½ [2 2 4 0 1 1] |
u12 | ½ [2 2 4 0 0 0] |
u13 | ½ [2 2 6 1 1 1] |
u14 | ½ [4 4 4 2 2 2] |
u15 | ½ [4 4 4 2 0 0] |
u16 | ½ [2 6 6 0 0 2] |
u17 | ½ [4 4 4 0 0 0] |
u18 | ½ [8 8 8 4 4 4] |
g1 | g2 | g3 | g4 | g5 | g6 | g7 | |
f1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
f2 | -16320 | 3617 | 0 | 0 | 0 | 0 | 0 |
f3 | 618231171506613408000+227210488606944000*a | -267246255594540097273-19043390810061389*a | 67070371115332644380+1085208873544246090*a | 50325919817262092891/2-(46088807071881137*a)/2 | 0 | 0 | 0 |
f4 | 618231171506613408000-227210488606944000*a | -267246255594540097273+19043390810061389*a | 67070371115332644380-1085208873544246090*a | 50325919817262092891/2+(46088807071881137*a)/2 | 0 | 0 | 0 |
f5 | -232305640344576000-414865732608000*b | 138253406219347982+171744054097106*b | -212246003659101076-1521538998472108*b | -21025941792756411+12242688184587*b | -679069732658152388-5454091892244604*b | 43773310206109883+324999624915189*b | 1065161531980287/2-(12704894680079*b)/2 |
f6 | -232305640344576000+414865732608000*b | 138253406219347982-171744054097106*b | -212246003659101076+1521538998472108*b | -21025941792756411-12242688184587*b | -679069732658152388+5454091892244604*b | 43773310206109883-324999624915189*b | 1065161531980287/2+(12704894680079*b)/2 |
f7 | 0 | 9548 | 117212 | -5630 | -177684 | -16796 | 663 |
f | λ2(f) | λ0,4(f) | λ1,4(f) | λ2,4(f) | λ3,4(f) |
f1 | 4398986092545 | 19344879779699286335320065 | 2066129936861886443520 | 31525678545371136 | 68719476736 |
f2 | 28996337880 | -44886989155960359360 | 295157308626991595520 | 13510963265273856 | 68719476736 |
f3 | 438096096-786528*a | 94188059140405248-214034505836544*a | 20644074072834048-158347569659904*a | 4504298163535872-4831838208*a | 68719476736 |
f4 | 438096096+786528*a | 94188059140405248+214034505836544*a | 20644074072834048+158347569659904*a | 4504298163535872+4831838208*a | 68719476736 |
f5 | 4414176-23328*b | -975014295552-64149387264*b | 8293015093248+7092043776*b | -252463546368-10871635968*b | 68719476736 |
f6 | 4414176+23328*b | -975014295552+64149387264*b | 8293015093248-7092043776*b | -252463546368+10871635968*b | 68719476736 |
f7 | -115200 | -784548495360 | -1062815662080 | -352724189184 | 68719476736 |
u | a(u; f1) | a(u; f2) | a(u; f3) | a(u; f4) | a(u; f5) | a(u; f6) | a(u; f7) |
u1 | 13912726954911229324966739363569/234258606489600 | 0 | 0 | 0 | 0 | 0 | 0 |
u2 | 3846482431548584275633602257/14354081280 | 2276253961922699242954470/899 | 0 | 0 | 0 | 0 | 0 |
u3 | 1273185684842581395234722347067/144990720 | 491670855775303036478165520/899 | 0 | 0 | 0 | 0 | 0 |
u4 | 445016619031983484355717/334080 | 25338634084482737398380 | 483157986848218883880234879523200000000-28209223026568228605703142400000000*a | 483157986848218883880234879523200000000+28209223026568228605703142400000000*a | 0 | 0 | 0 |
u5 | 15450190691937513287077/751680 | 16892422722988491598920/29 | 24905544975348089210819557696800000000+247552802513650699141158482400000000*a | 24905544975348089210819557696800000000-247552802513650699141158482400000000*a | 0 | 0 | 0 |
u6 | 238931060864446589481790370694277/334080 | 89262332025597759721315502880 | 18058420893973102154534879275029811200000000-47429390401038375315030866579558400000000*a | 18058420893973102154534879275029811200000000+47429390401038375315030866579558400000000*a | 0 | 0 | 0 |
u7 | 6356718306955926904241951341/576 | 2061551269113515514732196800 | 111436770719561850261806085538560000000000+10846211138376513620237348832000000000000*a | 111436770719561850261806085538560000000000-10846211138376513620237348832000000000000*a | 0 | 0 | 0 |
u8 | 12190127397766275077/27840 | 721921431676109104440/29 | 2604502478552571003744671574240000000+21088490054022689088097026720000000*a | 2604502478552571003744671574240000000-21088490054022689088097026720000000*a | -12125907806305888678654771200000000-100476340305194890926489600000000*b | -12125907806305888678654771200000000+100476340305194890926489600000000*b | -4157776806543360000000 |
u9 | 1334576754702420920447/10440 | 141475939134761300509440/29 | 296894024926670840078363672759040000000+1513925324309992699860332497920000000*a | 296894024926670840078363672759040000000-1513925324309992699860332497920000000*a | 170529502411664191984553164800000000+1062933915860219635590758400000000*b | 170529502411664191984553164800000000-1062933915860219635590758400000000*b | -66524428904693760000000 |
u10 | 1377484395947589083701/192 | 205984380083620256118000 | 7919096816549729321044803690220800000000 | 7919096816549729321044803690220800000000 | 1070337435672181364395868160000000000 | 1070337435672181364395868160000000000 | 166311072261734400000000 |
u11 | 150807173281373564010511/72 | 40366273010495553569448000 | 791864423033672419749093215869228800000000-233117594182986961295991035692800000000*a | 791864423033672419749093215869228800000000+233117594182986961295991035692800000000*a | -11020879592086229499286388736000000000-152935566401380855031267328000000000*b | -11020879592086229499286388736000000000+152935566401380855031267328000000000*b | 9812353263442329600000000 |
u12 | 1090820713984965277377688919/9280 | 65026532102945284130881461840/29 | 43223205363538648899808599867851466240000000-52976653635889599832969771898880000000*a | 43223205363538648899808599867851466240000000+52976653635889599832969771898880000000*a | 242261105918246462348982013132800000000+1150380061296361883820254822400000000*b | 242261105918246462348982013132800000000-1150380061296361883820254822400000000*b | -116151652867595304960000000 |
u13 | 3272262418907610829482205189/27840 | 96577547038180003026782230680/29 | 142330277070126411744442458520122576480000000+1415404302474581345353841554660359840000000*a | 142330277070126411744442458520122576480000000-1415404302474581345353841554660359840000000*a | 98228124020353346971283069337600000000+965165148514827891198708940800000000*b | 98228124020353346971283069337600000000-965165148514827891198708940800000000*b | 87679197296386375680000000 |
u14 | 369810790745246434330583900725/192 | 720142843396072028244172660800 | 224439289510383052344645386210015385600000000+7190271037751172618483818431295846400000000*a | 224439289510383052344645386210015385600000000-7190271037751172618483818431295846400000000*a | -19613800668394383160677438062592000000000-160647072637520191754669654016000000000*b | -19613800668394383160677438062592000000000+160647072637520191754669654016000000000*b | -883444415854333132800000000 |
u15 | 13494821101130248089117673766917/24 | 140466032027661424127888913868800 | 49463705768742128489150340773605212364800000000+435458408572858220652966465486044160000000000*a | 49463705768742128489150340773605212364800000000-435458408572858220652966465486044160000000000*a | 572083781107911581064223631867904000000000+4472409628597234492786241175552000000000*b | 572083781107911581064223631867904000000000-4472409628597234492786241175552000000000*b | -233484779592537971097600000000 |
u16 | 878444873863123742803518491442733061/27840 | 298020183573546453789287492422528080 | -3936024893458032280711494867527033044039680000000+13566021676279545626164986029506781890560000000*a | -3936024893458032280711494867527033044039680000000-13566021676279545626164986029506781890560000000*a | -3114087563267192904255296442571161600000000-18268308838255166832865625033932800000000*b | -3114087563267192904255296442571161600000000+18268308838255166832865625033932800000000*b | 187632950018835606405120000000 |
u17 | 878552105902591320830145827774226437/27840 | 171612798856686535022883868487667840/29 | 2406722333756897075236081698109007547555840000000-6230119875909471403207087066517712199680000000*a | 2406722333756897075236081698109007547555840000000+6230119875909471403207087066517712199680000000*a | 398360677098702239144879263108300800000000-39754865972261951668032145824153600000000*b | 398360677098702239144879263108300800000000+39754865972261951668032145824153600000000*b | 3393431341854815724503040000000 |
u18 | 47166907736321820129294279409727089843757057/5568 | 179279409193883951374180310983246649433600/29 | -112151340325452273263193428510925045680013312000000000+1597781114251498211836657103258324370849792000000000*a | -112151340325452273263193428510925045680013312000000000-1597781114251498211836657103258324370849792000000000*a | 34508362946076319850206581605561008128000000000+432548397471087937645615221911322624000000000*b | 34508362946076319850206581605561008128000000000-432548397471087937645615221911322624000000000*b | -18937233499065791608258560000000000 |
f | Q2(f, x, st)/(1-x) |
f1 | (1-32768*x)*(1-16384*x)*(1-8192*x)*(1-x/8192)*(1-x/16384)*(1-x/32768) |
f2 | (1-16384*x)*(1-8192*x)*(1-x/8192)*(1-x/16384)*(1+(295*x)/512+x^2) |
f3 | (1-8192*x)*(1-x/8192)*(1+(-135/1024+(3*a)/1024)*x+x^2/2)*(1+(-135/512+(3*a)/512)*x+2*x^2) |
f4 | (1-8192*x)*(1-x/8192)*(1+(-135/1024-(3*a)/1024)*x+x^2/2)*(1+(-135/512-(3*a)/512)*x+2*x^2) |
f5 | (1+(1035/4096+(27*b)/4096)*x+x^2/2)*(1+(295*x)/512+x^2)*(1+(1035/2048+(27*b)/2048)*x+2*x^2) |
f6 | (1+(1035/4096-(27*b)/4096)*x+x^2/2)*(1+(295*x)/512+x^2)*(1+(1035/2048-(27*b)/2048)*x+2*x^2) |
f7 | 1+(1553*x)/1024+(801709*x^2)/524288+(33924479*x^3)/16777216+(801709*x^4)/524288+(1553*x^5)/1024+x^6 |
f | Q2(f, x, spin) |
f1 | (1-4398046511104*x)*(1-536870912*x)*(1-268435456*x)*(1-134217728*x)*(1-32768*x)*(1-16384*x)*(1-8192*x)*(1-x) |
f2 | (1-216*x+32768*x^2)*(1-1769472*x+2199023255552*x^2)*(1-3538944*x+8796093022208*x^2)*(1-28991029248*x+590295810358705651712*x^2) |
f3 | (1-268435456*x)*(1-134217728*x)*(1-32768*x)*(1-16384*x)*(1+(-4320+96*a)*x+536870912*x^2)*(1+(-35389440+786432*a)*x+36028797018963968*x^2) |
f4 | (1-268435456*x)*(1-134217728*x)*(1-32768*x)*(1-16384*x)*(1+(-4320-96*a)*x+536870912*x^2)*(1+(-35389440-786432*a)*x+36028797018963968*x^2) |
f5 | (1-1769472*x+2199023255552*x^2)*(1-3538944*x+8796093022208*x^2)*(1+(894240+23328*b)*x+(4987187888128+29302456320*b)*x^2+(3932909112089640960+102597629011034112*b)*x^3+19342813113834066795298816*x^4) |
f6 | (1-1769472*x+2199023255552*x^2)*(1-3538944*x+8796093022208*x^2)*(1+(894240-23328*b)*x+(4987187888128-29302456320*b)*x^2+(3932909112089640960-102597629011034112*b)*x^3+19342813113834066795298816*x^4) |
f7 | 1+115200*x-2216899379200*x^2-261738742992076800*x^3-14607292949518362064453632*x^4-1151139165437049900155220787200*x^5-42881070384040361610309278668895027200*x^6+9800132167323027747745188694034924489932800*x^7+374144419156711147060143317175368453031918731001856*x^8 |
c1 | 234258606489600/13912726954911229324966739363569 |
c2 | 899/8233210580274403161766317990 |
c3 | 171386347271814817925009/4418368140321970953739028698976047649078511651403559545543091402145750000000000000-(5057530809929307122556119*a)/113439392818696443251772692331860535366266247393960689552046100204391058375000000000000 |
c4 | 171386347271814817925009/4418368140321970953739028698976047649078511651403559545543091402145750000000000000+(5057530809929307122556119*a)/113439392818696443251772692331860535366266247393960689552046100204391058375000000000000 |
c5 | 438838105352209/1342056163286218925603818464281827305655810129920000000000000000000-(56365611095929823*b)/24437500677278760416319930416107793408686646655713280000000000000000000 |
c6 | 438838105352209/1342056163286218925603818464281827305655810129920000000000000000000+(56365611095929823*b)/24437500677278760416319930416107793408686646655713280000000000000000000 |
c7 | 1/1966378962886616678400000000 |