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: | $[9, 3, 3]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 2x - 55\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-2$ |
7 | $[7, 7, w - 7]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}1$ |
9 | $[9, 3, 3]$ | $\phantom{-}1$ |
19 | $[19, 19, w + 5]$ | $-e - 2$ |
19 | $[19, 19, w - 6]$ | $\phantom{-}e$ |
23 | $[23, 23, w + 8]$ | $\phantom{-}\frac{1}{2}e + \frac{7}{2}$ |
23 | $[23, 23, -w + 9]$ | $-\frac{1}{2}e + \frac{5}{2}$ |
25 | $[25, 5, 5]$ | $-2$ |
29 | $[29, 29, -w - 4]$ | $-\frac{1}{2}e - \frac{11}{2}$ |
29 | $[29, 29, w - 5]$ | $\phantom{-}\frac{1}{2}e - \frac{9}{2}$ |
37 | $[37, 37, -w - 3]$ | $-e + 2$ |
37 | $[37, 37, w - 4]$ | $\phantom{-}e + 4$ |
41 | $[41, 41, -w - 9]$ | $\phantom{-}\frac{1}{2}e - \frac{13}{2}$ |
41 | $[41, 41, w - 10]$ | $-\frac{1}{2}e - \frac{15}{2}$ |
43 | $[43, 43, -w - 2]$ | $\phantom{-}9$ |
43 | $[43, 43, w - 3]$ | $\phantom{-}9$ |
47 | $[47, 47, -w - 1]$ | $-\frac{3}{2}e - \frac{5}{2}$ |
47 | $[47, 47, w - 2]$ | $\phantom{-}\frac{3}{2}e + \frac{1}{2}$ |
53 | $[53, 53, 2w - 13]$ | $-e - 3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, 3]$ | $-1$ |