Base field \(\Q(\sqrt{33}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[27, 9, 6w - 21]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e$ |
| 2 | $[2, 2, -w + 3]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w - 7]$ | $\phantom{-}0$ |
| 11 | $[11, 11, 4w - 13]$ | $\phantom{-}e^{3} - 8e$ |
| 17 | $[17, 17, -2w + 5]$ | $-e^{3} + 6e$ |
| 17 | $[17, 17, 2w + 3]$ | $\phantom{-}e^{3} - 9e$ |
| 25 | $[25, 5, 5]$ | $-e^{2} + 5$ |
| 29 | $[29, 29, -2w + 3]$ | $-e^{3} + 7e$ |
| 29 | $[29, 29, 2w + 1]$ | $-2e$ |
| 31 | $[31, 31, -2w + 9]$ | $-e^{2} + 2$ |
| 31 | $[31, 31, 2w + 7]$ | $-e^{2} + 11$ |
| 37 | $[37, 37, -4w - 11]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, 4w - 15]$ | $\phantom{-}e^{2} - 1$ |
| 41 | $[41, 41, -10w + 33]$ | $-2e^{3} + 17e$ |
| 41 | $[41, 41, 6w - 19]$ | $\phantom{-}2e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{2} - 10$ |
| 67 | $[67, 67, 2w - 11]$ | $\phantom{-}2e^{2} - 7$ |
| 67 | $[67, 67, -2w - 9]$ | $-e^{2} + 11$ |
| 83 | $[83, 83, 4w + 5]$ | $-2e$ |
| 83 | $[83, 83, 4w - 9]$ | $-e^{3} + 13e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, 2w - 7]$ | $1$ |