Base field \(\Q(\sqrt{35}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 35\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 7x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{7}{2}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e^{3} + 5e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}e^{3} + 3e$ |
| 13 | $[13, 13, w + 10]$ | $\phantom{-}e^{3} + 3e$ |
| 17 | $[17, 17, w + 1]$ | $-\frac{3}{2}e^{3} - \frac{13}{2}e$ |
| 17 | $[17, 17, w + 16]$ | $-\frac{3}{2}e^{3} - \frac{13}{2}e$ |
| 19 | $[19, 19, w + 4]$ | $\phantom{-}2e^{2} + 10$ |
| 19 | $[19, 19, -w + 4]$ | $\phantom{-}2e^{2} + 10$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e$ |
| 23 | $[23, 23, w + 14]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e$ |
| 29 | $[29, 29, -w - 8]$ | $-2$ |
| 29 | $[29, 29, w - 8]$ | $-2$ |
| 31 | $[31, 31, -w - 2]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w - 2]$ | $\phantom{-}0$ |
| 43 | $[43, 43, w + 11]$ | $\phantom{-}e^{3} + 9e$ |
| 43 | $[43, 43, w + 32]$ | $\phantom{-}e^{3} + 9e$ |
| 59 | $[59, 59, 2w - 9]$ | $\phantom{-}4$ |
| 59 | $[59, 59, -2w - 9]$ | $\phantom{-}4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $-1$ |