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: | $[9, 3, 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $76$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 30x^{2} + 625\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{1}{10}e$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{20}e^{2} - \frac{3}{4}$ |
3 | $[3, 3, w + 2]$ | $-\frac{1}{20}e^{2} + \frac{3}{4}$ |
5 | $[5, 5, -2w + 15]$ | $\phantom{-}2$ |
11 | $[11, 11, 3w - 22]$ | $\phantom{-}0$ |
13 | $[13, 13, w + 4]$ | $\phantom{-}0$ |
13 | $[13, 13, w + 9]$ | $\phantom{-}0$ |
17 | $[17, 17, w + 2]$ | $-\frac{1}{25}e^{3} + \frac{1}{5}e$ |
17 | $[17, 17, w + 15]$ | $-\frac{1}{25}e^{3} + \frac{1}{5}e$ |
19 | $[19, 19, -w - 6]$ | $-\frac{1}{50}e^{3} + \frac{11}{10}e$ |
19 | $[19, 19, w - 6]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{11}{10}e$ |
23 | $[23, 23, w + 3]$ | $\phantom{-}\frac{1}{5}e^{2} - 3$ |
23 | $[23, 23, w + 20]$ | $-\frac{1}{5}e^{2} + 3$ |
47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{2}{5}e^{2} - 6$ |
47 | $[47, 47, w + 33]$ | $-\frac{2}{5}e^{2} + 6$ |
49 | $[49, 7, -7]$ | $-6$ |
67 | $[67, 67, w + 16]$ | $\phantom{-}\frac{3}{5}e^{2} - 9$ |
67 | $[67, 67, w + 51]$ | $-\frac{3}{5}e^{2} + 9$ |
73 | $[73, 73, w + 36]$ | $-\frac{2}{25}e^{3} + \frac{2}{5}e$ |
73 | $[73, 73, w + 37]$ | $-\frac{2}{25}e^{3} + \frac{2}{5}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-\frac{1}{20}e^{2} + \frac{3}{4}$ |
$3$ | $[3, 3, w + 2]$ | $\frac{1}{20}e^{2} - \frac{3}{4}$ |