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: | $[13, 13, -w + 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w - 3]$ | $\phantom{-}4$ |
8 | $[8, 2, 2]$ | $-3$ |
9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}3e$ |
13 | $[13, 13, w + 3]$ | $-2$ |
13 | $[13, 13, -w + 2]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}4e$ |
23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}0$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $-4e$ |
31 | $[31, 31, w^{2} - 2w - 9]$ | $-4e$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}e$ |
41 | $[41, 41, w^{2} - w - 1]$ | $-7e$ |
41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}7e$ |
41 | $[41, 41, w^{2} - w - 10]$ | $\phantom{-}2$ |
43 | $[43, 43, -2w - 3]$ | $-2e$ |
47 | $[47, 47, -w^{2} - w + 4]$ | $-4$ |
49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}12$ |
59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}0$ |
59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}7e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w + 2]$ | $-1$ |