Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, -w + 8]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 8x^{4} + 15x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $-e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 5$ |
5 | $[5, 5, -w + 8]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 1]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$ |
7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 9e$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + 4e$ |
13 | $[13, 13, w + 9]$ | $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} - 4e$ |
17 | $[17, 17, w]$ | $\phantom{-}e^{3} - 4e$ |
17 | $[17, 17, w + 16]$ | $-e^{3} + 4e$ |
31 | $[31, 31, -w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$ |
31 | $[31, 31, w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$ |
41 | $[41, 41, 3w - 22]$ | $-e^{4} + 5e^{2} - 6$ |
47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 11e$ |
47 | $[47, 47, w + 27]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 11e$ |
53 | $[53, 53, w + 14]$ | $-2e^{5} + 12e^{3} - 10e$ |
53 | $[53, 53, w + 38]$ | $\phantom{-}2e^{5} - 12e^{3} + 10e$ |
59 | $[59, 59, -w - 10]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{2} + 2$ |
59 | $[59, 59, w - 11]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{2} + 2$ |
61 | $[61, 61, 2w - 13]$ | $\phantom{-}2e^{4} - 9e^{2} - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w + 8]$ | $-1$ |