Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, w + 2]$ |
Dimension: | $20$ |
CM: | no |
Base change: | no |
Newspace dimension: | $150$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{20} - 38x^{18} + 578x^{16} - 4564x^{14} + 20458x^{12} - 53719x^{10} + 82626x^{8} - 72700x^{6} + 34125x^{4} - 7172x^{2} + 404\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 9]$ | $...$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $...$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}1$ |
5 | $[5, 5, w + 3]$ | $...$ |
7 | $[7, 7, w + 3]$ | $...$ |
7 | $[7, 7, w + 4]$ | $...$ |
13 | $[13, 13, w + 1]$ | $...$ |
13 | $[13, 13, w + 12]$ | $...$ |
43 | $[43, 43, -w - 6]$ | $...$ |
43 | $[43, 43, w - 6]$ | $...$ |
47 | $[47, 47, w + 19]$ | $...$ |
47 | $[47, 47, w + 28]$ | $...$ |
59 | $[59, 59, w + 16]$ | $...$ |
59 | $[59, 59, w + 43]$ | $...$ |
71 | $[71, 71, w + 24]$ | $...$ |
71 | $[71, 71, w + 47]$ | $...$ |
73 | $[73, 73, 3w - 28]$ | $...$ |
73 | $[73, 73, 12w - 107]$ | $...$ |
79 | $[79, 79, -w]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w + 2]$ | $-1$ |