Base field 3.3.1489.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w^{2} - 3w - 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 7x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-1$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $-1$ |
| 17 | $[17, 17, w - 1]$ | $\phantom{-}e^{3} - 4e$ |
| 19 | $[19, 19, -w^{2} + 2w + 6]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w^{2} + 2w + 10]$ | $-2$ |
| 19 | $[19, 19, -w + 3]$ | $-2e^{3} + 12e$ |
| 23 | $[23, 23, w - 2]$ | $-e^{3} + 5e$ |
| 27 | $[27, 3, 3]$ | $-e^{2} + 2$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $-2e$ |
| 31 | $[31, 31, w^{2} - 3w - 6]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $-2e$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $\phantom{-}2e^{3} - 14e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-3e^{3} + 22e$ |
| 43 | $[43, 43, w^{2} - 3w - 10]$ | $\phantom{-}e^{2} - 2$ |
| 47 | $[47, 47, -w - 4]$ | $-6$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}2e^{3} - 16e$ |
| 47 | $[47, 47, -2w^{2} + 3w + 17]$ | $-2e$ |
| 49 | $[49, 7, w^{2} - w - 10]$ | $\phantom{-}3e^{3} - 23e$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-e^{3} + 6e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} - 3w - 5]$ | $1$ |