Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w + 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-e$ |
| 7 | $[7, 7, w - 3]$ | $\phantom{-}2$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}3$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $-\frac{1}{2}e$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w + 2]$ | $-2$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{3}{2}e$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}8$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{3}{2}e$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-\frac{5}{2}e$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $-2e$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}2e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}4e$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $\phantom{-}6$ |
| 43 | $[43, 43, -2w - 3]$ | $\phantom{-}2e$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $\phantom{-}8$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}4$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{3}{2}e$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{7}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w + 3]$ | $-1$ |