Base field \(\Q(\sqrt{119}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 119\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 134x^{10} + 5271x^{8} + 68718x^{6} + 350973x^{4} + 620316x^{2} + 93636\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 11]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{2802821}{9257614313076}e^{11} + \frac{147392111}{4628807156538}e^{9} + \frac{1984004311}{3085871437692}e^{7} + \frac{2816518909}{1542935718846}e^{5} + \frac{136562548599}{342874604188}e^{3} + \frac{1653855784553}{514311906282}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{2802821}{9257614313076}e^{11} - \frac{147392111}{4628807156538}e^{9} - \frac{1984004311}{3085871437692}e^{7} - \frac{2816518909}{1542935718846}e^{5} - \frac{136562548599}{342874604188}e^{3} - \frac{1653855784553}{514311906282}e$ |
| 7 | $[7, 7, w]$ | $-\frac{2802821}{9257614313076}e^{11} - \frac{147392111}{4628807156538}e^{9} - \frac{1984004311}{3085871437692}e^{7} - \frac{2816518909}{1542935718846}e^{5} - \frac{136562548599}{342874604188}e^{3} - \frac{2168167690835}{514311906282}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1835306}{45380462319}e^{10} + \frac{232284454}{45380462319}e^{8} + \frac{2647327556}{15126820773}e^{6} + \frac{22104745187}{15126820773}e^{4} + \frac{12962770212}{5042273591}e^{2} - \frac{24355160544}{5042273591}$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{56625971}{2314403578269}e^{11} - \frac{7093182001}{2314403578269}e^{9} - \frac{313703057311}{3085871437692}e^{7} - \frac{2234271480077}{3085871437692}e^{5} + \frac{81119554199}{342874604188}e^{3} + \frac{3463678860973}{514311906282}e$ |
| 11 | $[11, 11, w + 8]$ | $-\frac{56625971}{2314403578269}e^{11} - \frac{7093182001}{2314403578269}e^{9} - \frac{313703057311}{3085871437692}e^{7} - \frac{2234271480077}{3085871437692}e^{5} + \frac{81119554199}{342874604188}e^{3} + \frac{3463678860973}{514311906282}e$ |
| 17 | $[17, 17, w]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w - 10]$ | $\phantom{-}\frac{1572013}{60507283092}e^{10} + \frac{97538069}{30253641546}e^{8} + \frac{1057591761}{10084547182}e^{6} + \frac{44361503317}{60507283092}e^{4} + \frac{8848429247}{5042273591}e^{2} + \frac{31986905323}{5042273591}$ |
| 19 | $[19, 19, -w - 10]$ | $-\frac{1572013}{60507283092}e^{10} - \frac{97538069}{30253641546}e^{8} - \frac{1057591761}{10084547182}e^{6} - \frac{44361503317}{60507283092}e^{4} - \frac{8848429247}{5042273591}e^{2} - \frac{31986905323}{5042273591}$ |
| 23 | $[23, 23, w + 2]$ | $\phantom{-}\frac{712150207}{9257614313076}e^{11} + \frac{94332476837}{9257614313076}e^{9} + \frac{300677850077}{771467859423}e^{7} + \frac{14446492151329}{3085871437692}e^{5} + \frac{6785685198027}{342874604188}e^{3} + \frac{11837130324769}{514311906282}e$ |
| 23 | $[23, 23, w + 21]$ | $\phantom{-}\frac{712150207}{9257614313076}e^{11} + \frac{94332476837}{9257614313076}e^{9} + \frac{300677850077}{771467859423}e^{7} + \frac{14446492151329}{3085871437692}e^{5} + \frac{6785685198027}{342874604188}e^{3} + \frac{11837130324769}{514311906282}e$ |
| 41 | $[41, 41, w + 18]$ | $-\frac{42105493}{4628807156538}e^{11} - \frac{2487248959}{2314403578269}e^{9} - \frac{22829825455}{771467859423}e^{7} + \frac{14779491179}{1542935718846}e^{5} + \frac{192645596404}{85718651047}e^{3} + \frac{1082021794958}{257155953141}e$ |
| 41 | $[41, 41, w + 23]$ | $\phantom{-}\frac{42105493}{4628807156538}e^{11} + \frac{2487248959}{2314403578269}e^{9} + \frac{22829825455}{771467859423}e^{7} - \frac{14779491179}{1542935718846}e^{5} - \frac{192645596404}{85718651047}e^{3} - \frac{1082021794958}{257155953141}e$ |
| 47 | $[47, 47, -3w + 32]$ | $-\frac{23559581}{181521849276}e^{10} - \frac{3057533533}{181521849276}e^{8} - \frac{37031865265}{60507283092}e^{6} - \frac{188302784849}{30253641546}e^{4} - \frac{162896349083}{10084547182}e^{2} + \frac{35548304781}{5042273591}$ |
| 47 | $[47, 47, 8w - 87]$ | $\phantom{-}\frac{23559581}{181521849276}e^{10} + \frac{3057533533}{181521849276}e^{8} + \frac{37031865265}{60507283092}e^{6} + \frac{188302784849}{30253641546}e^{4} + \frac{162896349083}{10084547182}e^{2} - \frac{35548304781}{5042273591}$ |
| 53 | $[53, 53, -2w + 23]$ | $-\frac{1307242}{15126820773}e^{10} - \frac{58208856}{5042273591}e^{8} - \frac{6793583060}{15126820773}e^{6} - \frac{27994667447}{5042273591}e^{4} - \frac{110042072220}{5042273591}e^{2} - \frac{77630950614}{5042273591}$ |
| 53 | $[53, 53, -13w + 142]$ | $-\frac{1307242}{15126820773}e^{10} - \frac{58208856}{5042273591}e^{8} - \frac{6793583060}{15126820773}e^{6} - \frac{27994667447}{5042273591}e^{4} - \frac{110042072220}{5042273591}e^{2} - \frac{77630950614}{5042273591}$ |
| 59 | $[59, 59, -5w + 54]$ | $-\frac{9680975}{90760924638}e^{10} - \frac{1254905743}{90760924638}e^{8} - \frac{7606130689}{15126820773}e^{6} - \frac{53095044745}{10084547182}e^{4} - \frac{188933166621}{10084547182}e^{2} - \frac{65257393855}{5042273591}$ |
| 59 | $[59, 59, 6w - 65]$ | $\phantom{-}\frac{9680975}{90760924638}e^{10} + \frac{1254905743}{90760924638}e^{8} + \frac{7606130689}{15126820773}e^{6} + \frac{53095044745}{10084547182}e^{4} + \frac{188933166621}{10084547182}e^{2} + \frac{65257393855}{5042273591}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 11]$ | $-1$ |