Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $78$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 3x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{3}e + 1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{3}e$ |
| 3 | $[3, 3, -2w + 19]$ | $-2$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}e + 3$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{4}{3}e + 4$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{4}{3}e$ |
| 17 | $[17, 17, w + 3]$ | $-2e$ |
| 17 | $[17, 17, w + 13]$ | $-2e - 6$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{2}{3}e$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{2}{3}e - 2$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{2}{3}e$ |
| 37 | $[37, 37, w + 34]$ | $-\frac{2}{3}e - 2$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}14$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}9$ |
| 59 | $[59, 59, 4w - 37]$ | $-9$ |
| 61 | $[61, 61, w + 28]$ | $\phantom{-}\frac{10}{3}e + 10$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{10}{3}e$ |
| 71 | $[71, 71, w + 22]$ | $-2e$ |
| 71 | $[71, 71, w + 48]$ | $-2e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{1}{3}e - 1$ |
| $2$ | $[2, 2, w + 1]$ | $-\frac{1}{3}e$ |