Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $114$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 2$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{1}{2}e^{3} + 3e - 1$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{1}{2}e^{3} + 3e + 1$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}4$ |
| 23 | $[23, 23, w + 4]$ | $\phantom{-}\frac{1}{2}e^{2} + e + 1$ |
| 23 | $[23, 23, w + 18]$ | $-\frac{1}{2}e^{2} + e - 1$ |
| 25 | $[25, 5, 5]$ | $-\frac{1}{2}e^{2} + 3$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 4e - 8$ |
| 29 | $[29, 29, w + 27]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 4e + 8$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{1}{4}e^{3} + 2e^{2} - 3e - 8$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{1}{4}e^{3} - 2e^{2} - 3e + 8$ |
| 43 | $[43, 43, -w - 11]$ | $-e^{2} + 2e + 1$ |
| 43 | $[43, 43, w - 12]$ | $-e^{2} - 2e + 1$ |
| 47 | $[47, 47, -w - 6]$ | $-\frac{3}{4}e^{3} - e^{2} + 6e - 2$ |
| 47 | $[47, 47, w - 7]$ | $\phantom{-}\frac{3}{4}e^{3} - e^{2} - 6e - 2$ |
| 59 | $[59, 59, -w - 5]$ | $\phantom{-}\frac{3}{4}e^{3} + 2e^{2} - 5e - 10$ |
| 59 | $[59, 59, w - 6]$ | $-\frac{3}{4}e^{3} + 2e^{2} + 5e - 10$ |
| 61 | $[61, 61, w + 16]$ | $-\frac{5}{4}e^{3} + 2e^{2} + 5e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |