Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13,13,w^{3} - 6w + 4]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 2x^{2} - 16x - 20\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, w^{3} - 5w + 3]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - 5w + 2]$ | $\phantom{-}2$ |
13 | $[13, 13, w + 1]$ | $-e + 2$ |
13 | $[13, 13, w^{3} - 6w + 4]$ | $-1$ |
16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{2} + 5$ |
17 | $[17, 17, w^{2} + w - 2]$ | $-e$ |
17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}3$ |
23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $-e + 4$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $-e + 4$ |
25 | $[25, 5, -w^{2} + 3]$ | $\phantom{-}e + 2$ |
25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $\phantom{-}e + 2$ |
29 | $[29, 29, -w^{2} - 2w + 3]$ | $-\frac{1}{2}e^{2} + e + 9$ |
29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $\phantom{-}\frac{1}{2}e^{2} - 2e - 9$ |
43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $\phantom{-}e^{2} + e - 11$ |
43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $-\frac{1}{2}e^{2} + 9$ |
53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $\phantom{-}e^{2} - 10$ |
53 | $[53, 53, w^{2} + 2w - 5]$ | $\phantom{-}e + 2$ |
61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $-e^{2} - e + 5$ |
61 | $[61, 61, w^{3} - 7w + 3]$ | $-\frac{1}{2}e^{2} - e - 1$ |
61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $-1$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13,13,w^{3} - 6w + 4]$ | $1$ |