Base field \(\Q(\sqrt{2}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[113,113,-2w - 11]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 8x^{3} + 8x^{2} + 8x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w + 1]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 2e + 1$ |
| 7 | $[7, 7, -2w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + e + 5$ |
| 9 | $[9, 3, 3]$ | $-e^{4} + 7e^{2} - 2e - 4$ |
| 17 | $[17, 17, 3w + 1]$ | $\phantom{-}e^{4} - e^{3} - 7e^{2} + 7e + 6$ |
| 17 | $[17, 17, 3w - 1]$ | $\phantom{-}e^{3} + e^{2} - 6e$ |
| 23 | $[23, 23, w + 5]$ | $\phantom{-}e^{4} - 7e^{2} + 6$ |
| 23 | $[23, 23, -w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 4e - 1$ |
| 25 | $[25, 5, 5]$ | $-e^{4} + e^{3} + 8e^{2} - 8e - 6$ |
| 31 | $[31, 31, 4w + 1]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + e - 9$ |
| 31 | $[31, 31, -4w + 1]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{7}{2}e^{2} - 7e - 3$ |
| 41 | $[41, 41, 2w - 7]$ | $\phantom{-}e^{2} - e - 2$ |
| 41 | $[41, 41, -2w - 7]$ | $-e^{4} + 5e^{2} + 2$ |
| 47 | $[47, 47, -w - 7]$ | $-e^{4} + \frac{1}{2}e^{3} + \frac{15}{2}e^{2} - 2e - 3$ |
| 47 | $[47, 47, w - 7]$ | $-2e^{3} + 10e - 4$ |
| 71 | $[71, 71, -6w - 1]$ | $-e^{4} - e^{3} + 8e^{2} + 2e - 12$ |
| 71 | $[71, 71, 6w - 1]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{7}{2}e^{2} - 5e - 7$ |
| 73 | $[73, 73, -7w - 5]$ | $\phantom{-}e^{4} + 2e^{3} - 9e^{2} - 10e + 12$ |
| 73 | $[73, 73, 7w - 5]$ | $-2e^{4} + 15e^{2} - e - 10$ |
| 79 | $[79, 79, -w - 9]$ | $\phantom{-}3e^{4} - 21e^{2} + 4e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $113$ | $[113,113,-2w - 11]$ | $1$ |