Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + 2w + 2]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} + 2x^{2} - 14x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 5 | $[5, 5, w - 1]$ | $-1$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e + 1$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w - 3]$ | $-\frac{1}{2}e^{2} - e + 2$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{1}{2}e^{2} + 8$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $-\frac{1}{2}e^{2} - 2e + 3$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-e + 4$ |
| 27 | $[27, 3, -3]$ | $-e^{2} - 2e + 10$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e - 4$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e - 4$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}2$ |
| 31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}\frac{1}{2}e^{2} + e - 1$ |
| 37 | $[37, 37, 2w - 5]$ | $-\frac{1}{2}e^{2} - e + 8$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $-\frac{3}{2}e^{2} - 4e + 11$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}e^{2} + 3e - 12$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{1}{2}e^{2} + 12$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e - 1$ |
| 71 | $[71, 71, w - 5]$ | $\phantom{-}3e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + 2w + 2]$ | $-1$ |