Base field 3.3.1076.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, 2w + 5]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 5x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $-1$ |
3 | $[3, 3, -w^{2} + 2w + 3]$ | $\phantom{-}e$ |
7 | $[7, 7, -2w^{2} + 5w + 5]$ | $-e^{3} + 5e$ |
9 | $[9, 3, -w^{2} + 5]$ | $\phantom{-}e^{3} - 5e$ |
13 | $[13, 13, -w^{2} + 3w + 1]$ | $-3e^{3} + 12e$ |
13 | $[13, 13, 2w + 5]$ | $-1$ |
13 | $[13, 13, w - 1]$ | $\phantom{-}e^{3} - 7e$ |
17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}e^{3} - 3e$ |
19 | $[19, 19, w^{2} - 2w - 5]$ | $\phantom{-}3e^{2} - 10$ |
29 | $[29, 29, w^{2} - 7]$ | $-e^{3} + 3e$ |
31 | $[31, 31, 2w^{2} - 3w - 11]$ | $-4e^{2} + 10$ |
49 | $[49, 7, -2w^{2} - 4w + 1]$ | $\phantom{-}5e^{3} - 20e$ |
59 | $[59, 59, w^{2} - 2w - 11]$ | $-2e^{2} + 6$ |
71 | $[71, 71, -2w + 7]$ | $\phantom{-}e^{2} - 14$ |
73 | $[73, 73, w^{2} - 3w - 13]$ | $-e^{2} + 2$ |
73 | $[73, 73, 2w^{2} - 2w - 17]$ | $\phantom{-}4e^{2} - 6$ |
73 | $[73, 73, -w^{2} - 4w - 5]$ | $-3e^{2} + 6$ |
79 | $[79, 79, 2w - 1]$ | $-4e^{3} + 16e$ |
79 | $[79, 79, w^{2} + w - 5]$ | $\phantom{-}3e$ |
79 | $[79, 79, w - 5]$ | $-3e^{2} + 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, 2w + 5]$ | $1$ |