Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[36, 6, 6]$ |
Dimension: | $18$ |
CM: | no |
Base change: | no |
Newspace dimension: | $97$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{18} - 10x^{17} - 20x^{16} + 459x^{15} - 349x^{14} - 8456x^{13} + 13746x^{12} + 81344x^{11} - 158624x^{10} - 449659x^{9} + 868133x^{8} + 1507490x^{7} - 2353882x^{6} - 3126152x^{5} + 2890112x^{4} + 3495520x^{3} - 1080176x^{2} - 1326288x - 5168\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-1$ |
7 | $[7, 7, w - 7]$ | $...$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}e$ |
9 | $[9, 3, 3]$ | $\phantom{-}1$ |
19 | $[19, 19, w + 5]$ | $...$ |
19 | $[19, 19, w - 6]$ | $...$ |
23 | $[23, 23, w + 8]$ | $...$ |
23 | $[23, 23, -w + 9]$ | $...$ |
25 | $[25, 5, 5]$ | $...$ |
29 | $[29, 29, -w - 4]$ | $...$ |
29 | $[29, 29, w - 5]$ | $...$ |
37 | $[37, 37, -w - 3]$ | $...$ |
37 | $[37, 37, w - 4]$ | $...$ |
41 | $[41, 41, -w - 9]$ | $...$ |
41 | $[41, 41, w - 10]$ | $...$ |
43 | $[43, 43, -w - 2]$ | $...$ |
43 | $[43, 43, w - 3]$ | $...$ |
47 | $[47, 47, -w - 1]$ | $...$ |
47 | $[47, 47, w - 2]$ | $...$ |
53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $1$ |
$9$ | $[9, 3, 3]$ | $-1$ |