Base field \(\Q(\zeta_{11})^+\)
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[197,197,-w^{4} + w^{3} + w^{2} - w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 7x^{2} + 16x - 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^{4} + 3w^{2} + 1]$ | $-2e^{3} + 2e^{2} + 14e - 14$ |
| 23 | $[23, 23, -w^{4} + 3w^{2} + w - 2]$ | $\phantom{-}2e^{3} - 2e^{2} - 16e + 16$ |
| 23 | $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}e^{2} + 2e - 4$ |
| 23 | $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-2e^{3} + 2e^{2} + 14e - 14$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}3e^{3} - 2e^{2} - 23e + 24$ |
| 32 | $[32, 2, 2]$ | $-e^{3} + 10e - 4$ |
| 43 | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ | $-2e - 2$ |
| 43 | $[43, 43, -w^{4} + 2w^{2} + w + 1]$ | $-2e^{2} + 10$ |
| 43 | $[43, 43, w^{3} + w^{2} - 4w - 2]$ | $-e^{2} - 2e + 9$ |
| 43 | $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ | $\phantom{-}2e^{3} - 2e^{2} - 14e + 12$ |
| 43 | $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ | $-2e^{2} + 10$ |
| 67 | $[67, 67, 2w^{4} - 7w^{2} + 2]$ | $\phantom{-}4e^{3} - 4e^{2} - 30e + 28$ |
| 67 | $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ | $-2e^{3} + 14e - 4$ |
| 67 | $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ | $\phantom{-}2e^{2} - 10$ |
| 67 | $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ | $\phantom{-}2e^{3} - 3e^{2} - 18e + 25$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-2e^{3} + 2e^{2} + 12e - 16$ |
| 89 | $[89, 89, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}4e^{2} + 2e - 20$ |
| 89 | $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ | $-4e^{3} + 4e^{2} + 34e - 30$ |
| 89 | $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ | $\phantom{-}2e^{3} - e^{2} - 16e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $197$ | $[197,197,-w^{4} + w^{3} + w^{2} - w + 4]$ | $-1$ |