Base field \(\Q(\sqrt{6}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[19,19,-w + 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 3]$ | $-\frac{1}{2}e^{2} + \frac{7}{2}$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e$ |
| 19 | $[19, 19, w + 5]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{7}{2}$ |
| 19 | $[19, 19, -w + 5]$ | $-1$ |
| 23 | $[23, 23, -2w + 1]$ | $-2e$ |
| 23 | $[23, 23, -2w - 1]$ | $-\frac{3}{2}e^{3} + \frac{13}{2}e$ |
| 29 | $[29, 29, -3w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$ |
| 29 | $[29, 29, -3w - 5]$ | $-e^{3} + 9e$ |
| 43 | $[43, 43, -w - 7]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{9}{2}$ |
| 43 | $[43, 43, w - 7]$ | $-2e^{2} + 12$ |
| 47 | $[47, 47, 4w - 7]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{15}{2}e$ |
| 47 | $[47, 47, 6w - 13]$ | $\phantom{-}2e^{3} - 12e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{2} - 8$ |
| 53 | $[53, 53, -3w - 1]$ | $\phantom{-}2e^{3} - 10e$ |
| 53 | $[53, 53, 3w - 1]$ | $-e^{3} + 7e$ |
| 67 | $[67, 67, -7w + 19]$ | $\phantom{-}\frac{7}{2}e^{2} - \frac{27}{2}$ |
| 67 | $[67, 67, -3w + 11]$ | $-\frac{7}{2}e^{2} + \frac{39}{2}$ |
| 71 | $[71, 71, -4w - 5]$ | $-2e^{3} + 12e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w + 5]$ | $1$ |