Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 54x^{2} + 529\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{230}e^{3} - \frac{77}{230}e$ |
| 4 | $[4, 2, 2]$ | $-2$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{2}{115}e^{3} - \frac{154}{115}e$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{1}{23}e^{3} - \frac{54}{23}e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}\frac{1}{5}e^{2} + \frac{27}{5}$ |
| 23 | $[23, 23, w + 4]$ | $\phantom{-}\frac{13}{115}e^{3} + \frac{426}{115}e$ |
| 23 | $[23, 23, w + 18]$ | $\phantom{-}\frac{12}{115}e^{3} + \frac{349}{115}e$ |
| 25 | $[25, 5, 5]$ | $-1$ |
| 29 | $[29, 29, w + 1]$ | $-\frac{11}{115}e^{3} - \frac{387}{115}e$ |
| 29 | $[29, 29, w + 27]$ | $-\frac{9}{115}e^{3} - \frac{233}{115}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{11}{230}e^{3} + \frac{157}{230}e$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{19}{230}e^{3} - \frac{773}{230}e$ |
| 43 | $[43, 43, -w - 11]$ | $-\frac{1}{5}e^{2} - \frac{62}{5}$ |
| 43 | $[43, 43, w - 12]$ | $\phantom{-}\frac{1}{5}e^{2} - \frac{8}{5}$ |
| 47 | $[47, 47, -w - 6]$ | $-\frac{3}{10}e^{2} - \frac{61}{10}$ |
| 47 | $[47, 47, w - 7]$ | $-\frac{3}{10}e^{2} - \frac{101}{10}$ |
| 59 | $[59, 59, -w - 5]$ | $\phantom{-}\frac{3}{10}e^{2} + \frac{181}{10}$ |
| 59 | $[59, 59, w - 6]$ | $\phantom{-}\frac{3}{10}e^{2} - \frac{19}{10}$ |
| 61 | $[61, 61, w + 16]$ | $-\frac{3}{46}e^{3} - \frac{93}{46}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $\frac{1}{230}e^{3} + \frac{77}{230}e$ |