Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[7, 7, w]$ |
Dimension: | $2$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $132$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{2}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{2}e$ |
5 | $[5, 5, -3w + 25]$ | $\phantom{-}4$ |
7 | $[7, 7, w]$ | $-\frac{1}{2}e$ |
11 | $[11, 11, w - 9]$ | $-3$ |
11 | $[11, 11, -w - 9]$ | $-3$ |
17 | $[17, 17, w + 6]$ | $-\frac{7}{2}e$ |
17 | $[17, 17, w + 11]$ | $-\frac{7}{2}e$ |
23 | $[23, 23, w + 1]$ | $-3e$ |
23 | $[23, 23, w + 22]$ | $-3e$ |
31 | $[31, 31, 4w - 33]$ | $-2$ |
31 | $[31, 31, 4w + 33]$ | $-2$ |
37 | $[37, 37, w + 12]$ | $\phantom{-}e$ |
37 | $[37, 37, w + 25]$ | $\phantom{-}e$ |
53 | $[53, 53, w + 21]$ | $-3e$ |
53 | $[53, 53, w + 32]$ | $-3e$ |
61 | $[61, 61, -w - 3]$ | $\phantom{-}8$ |
61 | $[61, 61, w - 3]$ | $\phantom{-}8$ |
73 | $[73, 73, w + 17]$ | $\phantom{-}3e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w]$ | $\frac{1}{2}e$ |