Base field \(\Q(\zeta_{16})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[62,62,2w^{3} - w^{2} - 5w + 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 4x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{3} - w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{3} - w^{2} - 3w + 1]$ | $-2e + 4$ |
| 17 | $[17, 17, w^{2} - w - 3]$ | $-2e + 4$ |
| 31 | $[31, 31, w^{3} + w^{2} - 2w - 3]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}2e - 4$ |
| 31 | $[31, 31, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}2e - 4$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 2w - 3]$ | $-e$ |
| 47 | $[47, 47, -2w^{3} + w^{2} + 5w - 1]$ | $-2$ |
| 47 | $[47, 47, 2w^{3} + w^{2} - 6w - 1]$ | $-2$ |
| 47 | $[47, 47, -2w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}3e - 6$ |
| 47 | $[47, 47, 2w^{3} + w^{2} - 5w - 1]$ | $-2$ |
| 49 | $[49, 7, w^{2} + 1]$ | $\phantom{-}0$ |
| 49 | $[49, 7, -2w^{2} + 3]$ | $\phantom{-}3e - 4$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $-e - 2$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 2w - 5]$ | $-e - 2$ |
| 79 | $[79, 79, w^{3} + w^{2} - 2w - 5]$ | $-4e + 2$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w - 1]$ | $-2e + 16$ |
| 81 | $[81, 3, -3]$ | $-4e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w^{3} + 3w]$ | $-1$ |
| $31$ | $[31,31,-w^{3} - w^{2} + 2w + 3]$ | $-1$ |