Base field \(\Q(\sqrt{19}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15,15,-4w - 17]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 5x^{2} + 2x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w - 13]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 4]$ | $\phantom{-}e^{2} - e - 2$ |
| 3 | $[3, 3, w - 4]$ | $\phantom{-}1$ |
| 5 | $[5, 5, 2w + 9]$ | $\phantom{-}e^{3} - e^{2} - 4e$ |
| 5 | $[5, 5, -2w + 9]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w + 6]$ | $-e^{3} + 4e^{2} - 10$ |
| 17 | $[17, 17, -w + 6]$ | $-e^{2} + 2e + 2$ |
| 19 | $[19, 19, w]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 4$ |
| 31 | $[31, 31, 20w + 87]$ | $\phantom{-}2e^{3} - 2e^{2} - 9e + 4$ |
| 31 | $[31, 31, 7w + 30]$ | $\phantom{-}e^{3} - e^{2} - 3e + 4$ |
| 49 | $[49, 7, -7]$ | $-3e^{3} + 3e^{2} + 10e - 2$ |
| 59 | $[59, 59, 6w + 25]$ | $\phantom{-}e^{3} - 5e + 10$ |
| 59 | $[59, 59, -6w + 25]$ | $-2e^{3} + 3e^{2} + 5e - 4$ |
| 61 | $[61, 61, -9w - 40]$ | $\phantom{-}e^{3} - 8e + 2$ |
| 61 | $[61, 61, 9w - 40]$ | $\phantom{-}2e^{3} - 5e^{2} - 6e + 14$ |
| 67 | $[67, 67, 2w - 3]$ | $\phantom{-}3e^{3} - 3e^{2} - 8e$ |
| 67 | $[67, 67, -2w - 3]$ | $-4e^{2} - e + 12$ |
| 71 | $[71, 71, 3w + 10]$ | $-2e^{3} + 9e + 4$ |
| 71 | $[71, 71, 3w - 10]$ | $-2e^{3} + e^{2} + 13e + 2$ |
| 73 | $[73, 73, 27w + 118]$ | $\phantom{-}6e^{3} - 7e^{2} - 18e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 4]$ | $-1$ |
| $5$ | $[5,5,-2w + 9]$ | $-1$ |