Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[36, 6, 6]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 12x^{2} - 22x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, -w + 5]$ | $\phantom{-}e$ |
5 | $[5, 5, -w - 4]$ | $\phantom{-}e$ |
9 | $[9, 3, 3]$ | $-1$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}e^{2} - e - 6$ |
13 | $[13, 13, w - 4]$ | $\phantom{-}e^{2} - e - 6$ |
17 | $[17, 17, w + 6]$ | $-e - 1$ |
17 | $[17, 17, -w + 7]$ | $-e - 1$ |
19 | $[19, 19, w + 2]$ | $-e^{3} + e^{2} + 9e + 1$ |
19 | $[19, 19, w - 3]$ | $-e^{3} + e^{2} + 9e + 1$ |
23 | $[23, 23, w + 1]$ | $\phantom{-}e^{2} - e - 6$ |
23 | $[23, 23, -w + 2]$ | $\phantom{-}e^{2} - e - 6$ |
31 | $[31, 31, -w - 7]$ | $-e - 2$ |
31 | $[31, 31, w - 8]$ | $-e - 2$ |
37 | $[37, 37, 2w - 9]$ | $-2e^{3} + e^{2} + 23e + 16$ |
37 | $[37, 37, 2w + 7]$ | $-2e^{3} + e^{2} + 23e + 16$ |
43 | $[43, 43, 4w + 17]$ | $-2e^{3} + 25e + 21$ |
43 | $[43, 43, 4w - 21]$ | $-2e^{3} + 25e + 21$ |
47 | $[47, 47, -w - 8]$ | $-e^{2} + e + 8$ |
47 | $[47, 47, w - 9]$ | $-e^{2} + e + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $1$ |
$9$ | $[9, 3, 3]$ | $1$ |