Base field \(\Q(\sqrt{55}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, -2w + 15]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 28x^{2} + 100\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{9}{10}e$ |
3 | $[3, 3, w + 2]$ | $-\frac{1}{20}e^{3} + \frac{9}{10}e$ |
5 | $[5, 5, -2w + 15]$ | $\phantom{-}1$ |
11 | $[11, 11, 3w - 22]$ | $-\frac{1}{20}e^{3} + \frac{19}{10}e$ |
13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{7}{2}$ |
13 | $[13, 13, w + 9]$ | $-\frac{1}{4}e^{2} + \frac{7}{2}$ |
17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{3}{4}e^{2} - \frac{21}{2}$ |
17 | $[17, 17, w + 15]$ | $-\frac{3}{4}e^{2} + \frac{21}{2}$ |
19 | $[19, 19, -w - 6]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{19}{10}e$ |
19 | $[19, 19, w - 6]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{19}{10}e$ |
23 | $[23, 23, w + 3]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{9}{10}e$ |
23 | $[23, 23, w + 20]$ | $-\frac{1}{20}e^{3} + \frac{9}{10}e$ |
47 | $[47, 47, w + 14]$ | $-\frac{1}{4}e^{3} + \frac{9}{2}e$ |
47 | $[47, 47, w + 33]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{9}{2}e$ |
49 | $[49, 7, -7]$ | $-2$ |
67 | $[67, 67, w + 16]$ | $\phantom{-}\frac{9}{20}e^{3} - \frac{81}{10}e$ |
67 | $[67, 67, w + 51]$ | $-\frac{9}{20}e^{3} + \frac{81}{10}e$ |
73 | $[73, 73, w + 36]$ | $-\frac{3}{4}e^{2} + \frac{21}{2}$ |
73 | $[73, 73, w + 37]$ | $\phantom{-}\frac{3}{4}e^{2} - \frac{21}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -2w + 15]$ | $-1$ |