Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10,10,-w + 3]$ |
| Dimension: | $26$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $116$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{26} + 39x^{24} + 669x^{22} + 6657x^{20} + 42685x^{18} + 185341x^{16} + 557590x^{14} + 1169290x^{12} + 1695897x^{10} + 1663176x^{8} + 1057203x^{6} + 404658x^{4} + 81729x^{2} + 6561\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, -4w + 37]$ | $-1$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 17 | $[17, 17, w + 6]$ | $...$ |
| 17 | $[17, 17, w + 10]$ | $...$ |
| 19 | $[19, 19, -2w + 19]$ | $...$ |
| 19 | $[19, 19, -2w - 17]$ | $...$ |
| 23 | $[23, 23, w + 5]$ | $...$ |
| 23 | $[23, 23, w + 17]$ | $...$ |
| 37 | $[37, 37, w + 1]$ | $...$ |
| 37 | $[37, 37, w + 35]$ | $...$ |
| 41 | $[41, 41, -22w + 203]$ | $...$ |
| 41 | $[41, 41, -6w + 55]$ | $...$ |
| 43 | $[43, 43, w + 20]$ | $...$ |
| 43 | $[43, 43, w + 22]$ | $...$ |
| 53 | $[53, 53, w + 13]$ | $...$ |
| 53 | $[53, 53, w + 39]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $-\frac{2950363}{324654318}e^{25} - \frac{18763742}{54109053}e^{23} - \frac{626746543}{108218106}e^{21} - \frac{3016953439}{54109053}e^{19} - \frac{111401512963}{324654318}e^{17} - \frac{229749122954}{162327159}e^{15} - \frac{647813574668}{162327159}e^{13} - \frac{1250512555352}{162327159}e^{11} - \frac{120589920659}{12024234}e^{9} - \frac{919823750335}{108218106}e^{7} - \frac{79080911266}{18036351}e^{5} - \frac{21786688718}{18036351}e^{3} - \frac{519933343}{4008078}e$ |
| $5$ | $[5,5,4w + 33]$ | $1$ |