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: | $[13,13,-w + 4]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - x^{11} - 27x^{10} + 31x^{9} + 217x^{8} - 319x^{7} - 528x^{6} + 969x^{5} + 191x^{4} - 784x^{3} + 255x^{2} - 8x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 5]$ | $...$ |
5 | $[5, 5, -w - 4]$ | $...$ |
9 | $[9, 3, 3]$ | $...$ |
13 | $[13, 13, w + 3]$ | $...$ |
13 | $[13, 13, w - 4]$ | $-1$ |
17 | $[17, 17, w + 6]$ | $...$ |
17 | $[17, 17, -w + 7]$ | $...$ |
19 | $[19, 19, w + 2]$ | $...$ |
19 | $[19, 19, w - 3]$ | $...$ |
23 | $[23, 23, w + 1]$ | $...$ |
23 | $[23, 23, -w + 2]$ | $...$ |
31 | $[31, 31, -w - 7]$ | $...$ |
31 | $[31, 31, w - 8]$ | $...$ |
37 | $[37, 37, 2w - 9]$ | $...$ |
37 | $[37, 37, 2w + 7]$ | $...$ |
43 | $[43, 43, 4w + 17]$ | $...$ |
43 | $[43, 43, 4w - 21]$ | $...$ |
47 | $[47, 47, -w - 8]$ | $...$ |
47 | $[47, 47, w - 9]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13,13,-w + 4]$ | $1$ |