Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}2$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-e$ |
| 11 | $[11, 11, w + 2]$ | $-e + 2$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $-e + 3$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $-3e$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}e + 3$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}2e - 4$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}e + 6$ |
| 31 | $[31, 31, w^{2} - 10]$ | $\phantom{-}3$ |
| 41 | $[41, 41, w + 4]$ | $\phantom{-}7$ |
| 41 | $[41, 41, w^{2} - 5]$ | $-e + 5$ |
| 41 | $[41, 41, -2w - 5]$ | $\phantom{-}3e + 4$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}e + 8$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $-4e$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $-e + 1$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $-e - 6$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w + 1]$ | $-1$ |