Base field \(\Q(\zeta_{15})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[61,61,2w^{3} - w^{2} - 5w + 2]$ |
| Dimension: | $2$ |
| 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:
| \(x^{2} + 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{2} + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}e + 4$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}2e + 5$ |
| 29 | $[29, 29, -w^{3} - w^{2} + 2w + 3]$ | $\phantom{-}3e + 12$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-4e - 8$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 2]$ | $-4e - 8$ |
| 29 | $[29, 29, 2w^{3} + w^{2} - 7w]$ | $-4e - 8$ |
| 31 | $[31, 31, -2w + 1]$ | $\phantom{-}4e + 8$ |
| 31 | $[31, 31, 2w^{2} - 5]$ | $-4e - 6$ |
| 31 | $[31, 31, 2w^{3} + 2w^{2} - 6w - 3]$ | $\phantom{-}4e + 8$ |
| 31 | $[31, 31, 2w^{3} - 8w + 1]$ | $-4e - 6$ |
| 59 | $[59, 59, w^{3} + w^{2} - 2w - 5]$ | $\phantom{-}e - 8$ |
| 59 | $[59, 59, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}e - 8$ |
| 59 | $[59, 59, -3w^{3} + 10w - 4]$ | $-e + 4$ |
| 59 | $[59, 59, -2w^{3} - w^{2} + 7w - 2]$ | $-8e - 16$ |
| 61 | $[61, 61, 4w^{3} + w^{2} - 13w - 1]$ | $-8e - 14$ |
| 61 | $[61, 61, 2w^{3} - w^{2} - 5w + 2]$ | $-1$ |
| 61 | $[61, 61, -3w^{3} - w^{2} + 8w]$ | $\phantom{-}8e + 14$ |
| 61 | $[61, 61, 3w^{3} - w^{2} - 10w + 5]$ | $\phantom{-}0$ |
| 89 | $[89, 89, w^{3} + w^{2} - w - 4]$ | $-3e - 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $61$ | $[61,61,2w^{3} - w^{2} - 5w + 2]$ | $1$ |