Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[19,19,-w + 2]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 45x^{16} + 835x^{14} - 8234x^{12} + 46172x^{10} - 145064x^{8} + 231168x^{6} - 143744x^{4} + 23808x^{2} - 512\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{10221}{7785472}e^{17} - \frac{370341}{7785472}e^{15} + \frac{5145579}{7785472}e^{13} - \frac{16802823}{3892736}e^{11} + \frac{23705443}{1946368}e^{9} - \frac{2808297}{973184}e^{7} - \frac{5499655}{121648}e^{5} + \frac{6404441}{121648}e^{3} - \frac{118204}{7603}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{4487}{1946368}e^{16} + \frac{170153}{1946368}e^{14} - \frac{2544011}{1946368}e^{12} + \frac{593183}{60824}e^{10} - \frac{285123}{7603}e^{8} + \frac{8187305}{121648}e^{6} - \frac{4604901}{121648}e^{4} - \frac{95503}{30412}e^{2} + \frac{20555}{15206}$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{3495}{7785472}e^{17} - \frac{105739}{7785472}e^{15} + \frac{969149}{7785472}e^{13} + \frac{155993}{3892736}e^{11} - \frac{13947613}{1946368}e^{9} + \frac{41731971}{973184}e^{7} - \frac{23310959}{243296}e^{5} + \frac{8313567}{121648}e^{3} - \frac{304879}{30412}e$ |
| 7 | $[7, 7, w]$ | $-\frac{6311}{1946368}e^{17} + \frac{268971}{1946368}e^{15} - \frac{4709837}{1946368}e^{13} + \frac{21876303}{973184}e^{11} - \frac{57804775}{486592}e^{9} + \frac{85784457}{243296}e^{7} - \frac{32354601}{60824}e^{5} + \frac{9394797}{30412}e^{3} - \frac{299395}{7603}e$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}\frac{13545}{7785472}e^{17} - \frac{512909}{7785472}e^{15} + \frac{7691259}{7785472}e^{13} - \frac{29083429}{3892736}e^{11} + \frac{58135385}{1946368}e^{9} - \frac{58009631}{973184}e^{7} + \frac{11489369}{243296}e^{5} - \frac{228375}{121648}e^{3} - \frac{236383}{30412}e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}\frac{2241}{1946368}e^{17} - \frac{91973}{1946368}e^{15} + \frac{1541507}{1946368}e^{13} - \frac{6804493}{973184}e^{11} + \frac{16913049}{486592}e^{9} - \frac{23171523}{243296}e^{7} + \frac{7703165}{60824}e^{5} - \frac{1628049}{30412}e^{3} - \frac{17644}{7603}e$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{14467}{1946368}e^{16} + \frac{557541}{1946368}e^{14} - \frac{8570511}{1946368}e^{12} + \frac{8399397}{243296}e^{10} - \frac{17753689}{121648}e^{8} + \frac{39161727}{121648}e^{6} - \frac{40025521}{121648}e^{4} + \frac{3881337}{30412}e^{2} - \frac{100413}{15206}$ |
| 19 | $[19, 19, w - 2]$ | $-1$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}\frac{14121}{7785472}e^{17} - \frac{742593}{7785472}e^{15} + \frac{15782927}{7785472}e^{13} - \frac{87297627}{3892736}e^{11} + \frac{268529127}{1946368}e^{9} - \frac{450759653}{973184}e^{7} + \frac{92217209}{121648}e^{5} - \frac{53230643}{121648}e^{3} + \frac{383317}{7603}e$ |
| 23 | $[23, 23, w + 13]$ | $-\frac{13049}{3892736}e^{17} + \frac{549129}{3892736}e^{15} - \frac{9466039}{3892736}e^{13} + \frac{43172431}{1946368}e^{11} - \frac{111966235}{973184}e^{9} + \frac{164179497}{486592}e^{7} - \frac{3936446}{7603}e^{5} + \frac{20783475}{60824}e^{3} - \frac{504783}{7603}e$ |
| 37 | $[37, 37, w + 11]$ | $\phantom{-}\frac{18113}{7785472}e^{17} - \frac{544769}{7785472}e^{15} + \frac{4994719}{7785472}e^{13} + \frac{104401}{3892736}e^{11} - \frac{65205253}{1946368}e^{9} + \frac{191085767}{973184}e^{7} - \frac{25409483}{60824}e^{5} + \frac{32156941}{121648}e^{3} - \frac{351075}{15206}e$ |
| 37 | $[37, 37, w + 25]$ | $-\frac{11959}{3892736}e^{17} + \frac{514803}{3892736}e^{15} - \frac{9091781}{3892736}e^{13} + \frac{42477771}{1946368}e^{11} - \frac{112519703}{973184}e^{9} + \frac{167112257}{486592}e^{7} - \frac{63607535}{121648}e^{5} + \frac{19567713}{60824}e^{3} - \frac{681699}{15206}e$ |
| 59 | $[59, 59, 3w + 10]$ | $\phantom{-}\frac{8875}{973184}e^{16} - \frac{318411}{973184}e^{14} + \frac{4395317}{973184}e^{12} - \frac{14454965}{486592}e^{10} + \frac{21842969}{243296}e^{8} - \frac{8968975}{121648}e^{6} - \frac{996843}{7603}e^{4} + \frac{2025175}{15206}e^{2} - \frac{68986}{7603}$ |
| 59 | $[59, 59, 3w - 13]$ | $-\frac{27667}{973184}e^{16} + \frac{1048983}{973184}e^{14} - \frac{15742097}{973184}e^{12} + \frac{59494443}{486592}e^{10} - \frac{118582631}{243296}e^{8} + \frac{118104853}{121648}e^{6} - \frac{24860827}{30412}e^{4} + \frac{3767595}{15206}e^{2} - \frac{114552}{7603}$ |
| 73 | $[73, 73, w + 15]$ | $-\frac{43413}{3892736}e^{17} + \frac{1855445}{3892736}e^{15} - \frac{32540971}{3892736}e^{13} + \frac{151029387}{1946368}e^{11} - \frac{397221631}{973184}e^{9} + \frac{583262405}{486592}e^{7} - \frac{53896379}{30412}e^{5} + \frac{59959687}{60824}e^{3} - \frac{816583}{7603}e$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}\frac{27075}{3892736}e^{17} - \frac{1112815}{3892736}e^{15} + \frac{18626569}{3892736}e^{13} - \frac{81872311}{1946368}e^{11} + \frac{202548651}{973184}e^{9} - \frac{278799325}{486592}e^{7} + \frac{97229963}{121648}e^{5} - \frac{26842797}{60824}e^{3} + \frac{1136267}{15206}e$ |
| 89 | $[89, 89, -w - 10]$ | $-\frac{437}{60824}e^{16} + \frac{63655}{243296}e^{14} - \frac{899019}{243296}e^{12} + \frac{6161133}{243296}e^{10} - \frac{10264965}{121648}e^{8} + \frac{834606}{7603}e^{6} + \frac{47230}{7603}e^{4} - \frac{543219}{15206}e^{2} - \frac{3287}{7603}$ |
| 89 | $[89, 89, w - 11]$ | $-\frac{14759}{973184}e^{16} + \frac{560989}{973184}e^{14} - \frac{8435343}{973184}e^{12} + \frac{15935327}{243296}e^{10} - \frac{31537341}{121648}e^{8} + \frac{7640583}{15206}e^{6} - \frac{23380467}{60824}e^{4} + \frac{1361357}{15206}e^{2} - \frac{19975}{7603}$ |
| 97 | $[97, 97, w + 22]$ | $\phantom{-}\frac{3807}{3892736}e^{17} - \frac{388547}{3892736}e^{15} + \frac{11298949}{3892736}e^{13} - \frac{75329007}{1946368}e^{11} + \frac{261994411}{973184}e^{9} - \frac{479022261}{486592}e^{7} + \frac{208567657}{121648}e^{5} - \frac{63224961}{60824}e^{3} + \frac{1876181}{15206}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w + 2]$ | $1$ |