Base field 4.4.8112.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, w^{3} - 4w + 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 4x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
4 | $[4, 2, w^{2} - w - 1]$ | $\phantom{-}e - 1$ |
9 | $[9, 3, -w^{2} + 2]$ | $-e - 1$ |
13 | $[13, 13, w^{3} - 4w + 2]$ | $\phantom{-}1$ |
13 | $[13, 13, -w^{3} + 4w + 2]$ | $-e - 4$ |
17 | $[17, 17, w^{3} - 3w - 1]$ | $-2e^{2} + e + 4$ |
17 | $[17, 17, -w^{3} + 3w - 1]$ | $\phantom{-}e^{2} - 3e - 4$ |
29 | $[29, 29, w^{3} + w^{2} - 4w - 2]$ | $\phantom{-}e^{2} - 4$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e^{2} - 4$ |
43 | $[43, 43, w^{2} + w - 4]$ | $\phantom{-}3e$ |
43 | $[43, 43, w^{2} - w - 4]$ | $-2e^{2} - 4e + 4$ |
53 | $[53, 53, w^{3} - 2w - 2]$ | $-4e^{2} + 3e + 18$ |
53 | $[53, 53, -w^{3} + 2w - 2]$ | $\phantom{-}2e - 1$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}4e^{2} - 3e - 9$ |
79 | $[79, 79, -w^{3} - w^{2} + 4w + 1]$ | $-4e^{2} - 2e + 11$ |
101 | $[101, 101, -w^{3} + w^{2} + 3w - 5]$ | $-6e^{2} - 2e + 15$ |
101 | $[101, 101, w^{3} + w^{2} - 3w - 5]$ | $\phantom{-}4e^{2} + 4e - 9$ |
103 | $[103, 103, 2w^{2} - w - 4]$ | $-3e^{2} - 6e + 9$ |
103 | $[103, 103, 2w^{2} + w - 4]$ | $\phantom{-}3e^{2} - 14$ |
107 | $[107, 107, 2w^{2} + w - 5]$ | $-4e^{2} + 5e + 17$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w^{3} - 4w + 2]$ | $-1$ |