Base field \(\Q(\sqrt{110}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 110\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 58x^{2} + 625\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{50}e^{3} + \frac{33}{50}e$ |
| 9 | $[9, 3, 3]$ | $-3$ |
| 11 | $[11, 11, -w + 11]$ | $-2$ |
| 17 | $[17, 17, w + 5]$ | $-\frac{1}{50}e^{3} + \frac{83}{50}e$ |
| 17 | $[17, 17, w + 12]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{83}{50}e$ |
| 23 | $[23, 23, w + 8]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{33}{50}e$ |
| 23 | $[23, 23, w + 15]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{33}{50}e$ |
| 29 | $[29, 29, w + 9]$ | $\phantom{-}\frac{9}{100}e^{3} + \frac{1}{4}e^{2} - \frac{297}{100}e - \frac{29}{4}$ |
| 29 | $[29, 29, -w + 9]$ | $\phantom{-}\frac{9}{100}e^{3} - \frac{1}{4}e^{2} - \frac{297}{100}e + \frac{29}{4}$ |
| 37 | $[37, 37, w + 6]$ | $-\frac{11}{100}e^{3} + \frac{1}{4}e^{2} + \frac{363}{100}e - \frac{29}{4}$ |
| 37 | $[37, 37, w + 31]$ | $-\frac{11}{100}e^{3} - \frac{1}{4}e^{2} + \frac{363}{100}e + \frac{29}{4}$ |
| 43 | $[43, 43, w + 14]$ | $-\frac{1}{50}e^{3} + \frac{83}{50}e - 3$ |
| 43 | $[43, 43, w + 29]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{83}{50}e - 3$ |
| 47 | $[47, 47, w + 4]$ | $\phantom{-}\frac{3}{25}e^{3} - \frac{99}{25}e$ |
| 47 | $[47, 47, w + 43]$ | $\phantom{-}\frac{3}{25}e^{3} - \frac{99}{25}e$ |
| 49 | $[49, 7, -7]$ | $-3$ |
| 53 | $[53, 53, w + 2]$ | $-\frac{3}{100}e^{3} - \frac{3}{4}e^{2} + \frac{99}{100}e + \frac{87}{4}$ |
| 53 | $[53, 53, w + 51]$ | $-\frac{3}{100}e^{3} + \frac{3}{4}e^{2} + \frac{99}{100}e - \frac{87}{4}$ |
| 59 | $[59, 59, -w - 13]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{83}{50}e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |