Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, -w + 5]$ |
Dimension: | $8$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + 15x^{6} + 72x^{4} + 112x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{9}{2}e^{3} + 9e$ |
5 | $[5, 5, -w + 5]$ | $-1$ |
7 | $[7, 7, w + 3]$ | $-e^{3} - 5e$ |
7 | $[7, 7, w + 4]$ | $-e^{3} - 5e$ |
13 | $[13, 13, w + 2]$ | $-\frac{1}{4}e^{7} - \frac{13}{4}e^{5} - \frac{25}{2}e^{3} - 14e$ |
13 | $[13, 13, w + 11]$ | $-\frac{1}{4}e^{7} - \frac{13}{4}e^{5} - \frac{25}{2}e^{3} - 14e$ |
17 | $[17, 17, w + 8]$ | $-\frac{1}{2}e^{5} - \frac{11}{2}e^{3} - 14e$ |
17 | $[17, 17, w + 9]$ | $-\frac{1}{2}e^{5} - \frac{11}{2}e^{3} - 14e$ |
19 | $[19, 19, w + 7]$ | $-\frac{1}{2}e^{6} - \frac{9}{2}e^{4} - 9e^{2} - 2$ |
19 | $[19, 19, -w + 7]$ | $-\frac{1}{2}e^{6} - \frac{9}{2}e^{4} - 9e^{2} - 2$ |
29 | $[29, 29, -w - 1]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{9}{2}e^{4} + 7e^{2} - 6$ |
29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{9}{2}e^{4} + 7e^{2} - 6$ |
37 | $[37, 37, w + 17]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{17}{4}e^{5} + \frac{43}{2}e^{3} + 28e$ |
37 | $[37, 37, w + 20]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{17}{4}e^{5} + \frac{43}{2}e^{3} + 28e$ |
71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{11}{2}e^{4} + 18e^{2} + 12$ |
71 | $[71, 71, -2w - 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{11}{2}e^{4} + 18e^{2} + 12$ |
83 | $[83, 83, w + 14]$ | $-\frac{1}{2}e^{5} - \frac{13}{2}e^{3} - 19e$ |
83 | $[83, 83, w + 69]$ | $-\frac{1}{2}e^{5} - \frac{13}{2}e^{3} - 19e$ |
101 | $[101, 101, -7w + 37]$ | $-\frac{3}{2}e^{6} - \frac{31}{2}e^{4} - 39e^{2} - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w + 5]$ | $1$ |