Base field 6.6.1397493.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19,19,-w^{2} + w + 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 180x^{12} + 12844x^{10} - 462728x^{8} + 8881472x^{6} - 88352640x^{4} + 415220096x^{2} - 694863104\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $-\frac{7962101391}{16794592591143712}e^{12} + \frac{1292412140965}{16794592591143712}e^{10} - \frac{40057752701583}{8397296295571856}e^{8} + \frac{595298132405435}{4198648147785928}e^{6} - \frac{2193471582055581}{1049662036946482}e^{4} + \frac{14911331147038519}{1049662036946482}e^{2} - \frac{16849249680137060}{524831018473241}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{191074628995}{873318814739473024}e^{13} - \frac{17431559298865}{436659407369736512}e^{11} + \frac{47419749827977}{16794592591143712}e^{9} - \frac{5269295011775125}{54582425921217064}e^{7} + \frac{87886089791615585}{54582425921217064}e^{5} - \frac{78276131633521882}{6822803240152133}e^{3} + \frac{170728895325525653}{6822803240152133}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e$ |
| 19 | $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ | $\phantom{-}\frac{6909619973}{33589185182287424}e^{12} - \frac{311595722953}{8397296295571856}e^{10} + \frac{22032376316525}{8397296295571856}e^{8} - \frac{380718412305015}{4198648147785928}e^{6} + \frac{1611196657555359}{1049662036946482}e^{4} - \frac{5838789161964808}{524831018473241}e^{2} + \frac{15575332388535300}{524831018473241}$ |
| 19 | $[19, 19, w^{2} - w - 1]$ | $-1$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}\frac{12151965489}{8397296295571856}e^{12} - \frac{3495718236269}{16794592591143712}e^{10} + \frac{89891208316747}{8397296295571856}e^{8} - \frac{970055644354831}{4198648147785928}e^{6} + \frac{1859361353459373}{1049662036946482}e^{4} - \frac{342253568134937}{1049662036946482}e^{2} - \frac{10257429611498802}{524831018473241}$ |
| 37 | $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ | $-\frac{13184687323}{33589185182287424}e^{12} + \frac{190600891167}{4198648147785928}e^{10} - \frac{10979274284047}{8397296295571856}e^{8} - \frac{78046304921723}{4198648147785928}e^{6} + \frac{647199234364191}{524831018473241}e^{4} - \frac{7063672348315466}{524831018473241}e^{2} + \frac{20782399636047408}{524831018473241}$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ | $\phantom{-}\frac{18858232739}{54582425921217064}e^{13} - \frac{11281649374971}{218329703684868256}e^{11} + \frac{23803182899653}{8397296295571856}e^{9} - \frac{3733625695852607}{54582425921217064}e^{7} + \frac{8908246514811531}{13645606480304266}e^{5} - \frac{11790631830799495}{13645606480304266}e^{3} - \frac{59263759068708943}{6822803240152133}e$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $-\frac{71414769617}{436659407369736512}e^{13} + \frac{13599993447191}{436659407369736512}e^{11} - \frac{9666891339947}{4198648147785928}e^{9} + \frac{8957788251169583}{109164851842434128}e^{7} - \frac{77220597975805985}{54582425921217064}e^{5} + \frac{70945183850736022}{6822803240152133}e^{3} - \frac{182062033392757512}{6822803240152133}e$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{14053652799}{8397296295571856}e^{12} - \frac{4326298966911}{16794592591143712}e^{10} + \frac{15775159981099}{1049662036946482}e^{8} - \frac{1746583293039429}{4198648147785928}e^{6} + \frac{11811270971439321}{2099324073892964}e^{4} - \frac{18270672346694421}{524831018473241}e^{2} + \frac{40418812973390173}{524831018473241}$ |
| 71 | $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ | $-\frac{356429726631}{436659407369736512}e^{13} + \frac{7211103145661}{54582425921217064}e^{11} - \frac{68942227849115}{8397296295571856}e^{9} + \frac{13417815908892333}{54582425921217064}e^{7} - \frac{24836515486478519}{6822803240152133}e^{5} + \frac{165955641947778622}{6822803240152133}e^{3} - \frac{385394047060101670}{6822803240152133}e$ |
| 71 | $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ | $\phantom{-}\frac{641469522789}{873318814739473024}e^{13} - \frac{54981149627361}{436659407369736512}e^{11} + \frac{140262162211747}{16794592591143712}e^{9} - \frac{14613650188555439}{54582425921217064}e^{7} + \frac{229233055021109757}{54582425921217064}e^{5} - \frac{388262922876133725}{13645606480304266}e^{3} + \frac{414508449294241565}{6822803240152133}e$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ | $-\frac{4805708665}{13645606480304266}e^{13} + \frac{23949596881305}{436659407369736512}e^{11} - \frac{27087423511991}{8397296295571856}e^{9} + \frac{9730922102391045}{109164851842434128}e^{7} - \frac{64126367253688187}{54582425921217064}e^{5} + \frac{89820291907617917}{13645606480304266}e^{3} - \frac{61717520575958400}{6822803240152133}e$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ | $\phantom{-}\frac{48659232727}{33589185182287424}e^{12} - \frac{1013663882299}{4198648147785928}e^{10} + \frac{130511349418543}{8397296295571856}e^{8} - \frac{2036776782583389}{4198648147785928}e^{6} + \frac{3931909072507922}{524831018473241}e^{4} - \frac{26699073176154390}{524831018473241}e^{2} + \frac{58358903336415100}{524831018473241}$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ | $\phantom{-}\frac{48659232727}{33589185182287424}e^{12} - \frac{1013663882299}{4198648147785928}e^{10} + \frac{130511349418543}{8397296295571856}e^{8} - \frac{2036776782583389}{4198648147785928}e^{6} + \frac{3931909072507922}{524831018473241}e^{4} - \frac{26699073176154390}{524831018473241}e^{2} + \frac{58358903336415100}{524831018473241}$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ | $-\frac{4805708665}{13645606480304266}e^{13} + \frac{23949596881305}{436659407369736512}e^{11} - \frac{27087423511991}{8397296295571856}e^{9} + \frac{9730922102391045}{109164851842434128}e^{7} - \frac{64126367253688187}{54582425921217064}e^{5} + \frac{89820291907617917}{13645606480304266}e^{3} - \frac{54894717335806267}{6822803240152133}e$ |
| 89 | $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ | $\phantom{-}\frac{177398889643}{873318814739473024}e^{13} - \frac{13704684838753}{436659407369736512}e^{11} + \frac{30892671573009}{16794592591143712}e^{9} - \frac{1406307305770641}{27291212960608532}e^{7} + \frac{40118038629451697}{54582425921217064}e^{5} - \frac{75620578211282599}{13645606480304266}e^{3} + \frac{125707540260264096}{6822803240152133}e$ |
| 89 | $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ | $\phantom{-}\frac{177398889643}{873318814739473024}e^{13} - \frac{13704684838753}{436659407369736512}e^{11} + \frac{30892671573009}{16794592591143712}e^{9} - \frac{1406307305770641}{27291212960608532}e^{7} + \frac{40118038629451697}{54582425921217064}e^{5} - \frac{75620578211282599}{13645606480304266}e^{3} + \frac{125707540260264096}{6822803240152133}e$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ | $-\frac{278429405783}{436659407369736512}e^{13} + \frac{47202709112281}{436659407369736512}e^{11} - \frac{59391535381477}{8397296295571856}e^{9} + \frac{24435539693710893}{109164851842434128}e^{7} - \frac{191281120242696197}{54582425921217064}e^{5} + \frac{335737672612972791}{13645606480304266}e^{3} - \frac{414747885714843558}{6822803240152133}e$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ | $\phantom{-}\frac{159194614653}{873318814739473024}e^{13} - \frac{18691962231505}{436659407369736512}e^{11} + \frac{62143744080765}{16794592591143712}e^{9} - \frac{1008626164256840}{6822803240152133}e^{7} + \frac{149597747107956543}{54582425921217064}e^{5} - \frac{275809484889630545}{13645606480304266}e^{3} + \frac{286323636894643046}{6822803240152133}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w^{2} + w + 1]$ | $1$ |