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: | yes |
| 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:
| \(x^{4} - 44x^{2} + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{1}{5}e^{3} + \frac{44}{5}e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 4]$ | $-\frac{1}{15}e^{3} + \frac{64}{15}e$ |
| 23 | $[23, 23, w + 18]$ | $-\frac{4}{15}e^{3} + \frac{181}{15}e$ |
| 25 | $[25, 5, 5]$ | $-7$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{1}{15}e^{3} - \frac{19}{15}e$ |
| 29 | $[29, 29, w + 27]$ | $-\frac{1}{3}e^{3} + \frac{43}{3}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}0$ |
| 43 | $[43, 43, -w - 11]$ | $-\frac{1}{3}e^{2} + \frac{22}{3}$ |
| 43 | $[43, 43, w - 12]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{22}{3}$ |
| 47 | $[47, 47, -w - 6]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w - 7]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -w - 5]$ | $\phantom{-}0$ |
| 59 | $[59, 59, w - 6]$ | $\phantom{-}0$ |
| 61 | $[61, 61, w + 16]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |