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: | $[2,2,-w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - x^{2} + 7x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-1$ |
| 3 | $[3, 3, -2w + 19]$ | $\phantom{-}e^{3} - 2e^{2} - 3e + 4$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e^{3} - 2e^{2} - 3e + 6$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}e^{3} - e^{2} - 2e$ |
| 13 | $[13, 13, w + 1]$ | $-e^{3} + 5e - 1$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}4e^{3} - 6e^{2} - 11e + 11$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}2e^{3} - 4e^{2} - 4e + 9$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}2e^{3} - 5e^{2} - 6e + 12$ |
| 19 | $[19, 19, w + 6]$ | $-2e - 1$ |
| 19 | $[19, 19, w + 12]$ | $-e^{3} + 7e - 1$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}5e^{3} - 9e^{2} - 10e + 14$ |
| 37 | $[37, 37, w + 34]$ | $-2e^{3} + 6e^{2} + 4e - 10$ |
| 49 | $[49, 7, -7]$ | $-e^{3} + 2e^{2} + 3e - 13$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}2e^{3} - 2e^{2} - 4e + 3$ |
| 59 | $[59, 59, 4w - 37]$ | $-7e^{3} + 11e^{2} + 22e - 21$ |
| 61 | $[61, 61, w + 28]$ | $\phantom{-}4e^{2} - 2e - 13$ |
| 61 | $[61, 61, w + 32]$ | $\phantom{-}3e^{2} - 2e - 4$ |
| 71 | $[71, 71, w + 22]$ | $-e^{3} - e^{2} + 3e - 3$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}e^{3} + e^{2} - 8e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $1$ |