Base field \(\Q(\sqrt{65}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 16\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7,7,-w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 7x^{2} - x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-e^{2} + 4$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-e + 1$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}e^{2} - 1$ |
| 7 | $[7, 7, w + 5]$ | $-1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 5$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}e^{3} - e^{2} - 3e + 5$ |
| 29 | $[29, 29, -2w + 7]$ | $\phantom{-}e^{3} + e^{2} - 5e - 7$ |
| 29 | $[29, 29, 2w + 5]$ | $-3e^{3} + 3e^{2} + 12e - 8$ |
| 37 | $[37, 37, w + 9]$ | $-e^{3} + 5e + 2$ |
| 37 | $[37, 37, w + 27]$ | $-e^{3} + 2e + 3$ |
| 47 | $[47, 47, w + 10]$ | $\phantom{-}2e^{2} - e - 7$ |
| 47 | $[47, 47, w + 36]$ | $\phantom{-}e^{3} + 2e^{2} - 6e - 3$ |
| 61 | $[61, 61, 2w - 3]$ | $-2e^{3} + 3e^{2} + 8e - 15$ |
| 61 | $[61, 61, -2w - 1]$ | $\phantom{-}2e^{3} - 11e + 1$ |
| 67 | $[67, 67, w + 23]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 10$ |
| 67 | $[67, 67, w + 43]$ | $-3e^{3} + 3e^{2} + 10e - 12$ |
| 73 | $[73, 73, w + 24]$ | $\phantom{-}e^{3} + e^{2} - 3e - 1$ |
| 73 | $[73, 73, w + 48]$ | $\phantom{-}e^{3} - 3e^{2} - 4e + 14$ |
| 79 | $[79, 79, 2w - 13]$ | $\phantom{-}3e^{3} - 4e^{2} - 13e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w + 2]$ | $1$ |