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: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 24x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{16}e^{3} + 2e$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{1}{16}e^{3} - 2e$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{1}{16}e^{3} - e$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}\frac{1}{16}e^{3} + e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 4]$ | $\phantom{-}\frac{5}{16}e^{3} + 5e$ |
| 23 | $[23, 23, w + 18]$ | $-\frac{5}{16}e^{3} - 5e$ |
| 25 | $[25, 5, 5]$ | $-2$ |
| 29 | $[29, 29, w + 1]$ | $-\frac{1}{8}e^{3} - 2e$ |
| 29 | $[29, 29, w + 27]$ | $\phantom{-}\frac{1}{8}e^{3} + 2e$ |
| 31 | $[31, 31, w + 13]$ | $-\frac{1}{16}e^{3} - 2e$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{1}{16}e^{3} - 2e$ |
| 43 | $[43, 43, -w - 11]$ | $\phantom{-}4$ |
| 43 | $[43, 43, w - 12]$ | $\phantom{-}4$ |
| 47 | $[47, 47, -w - 6]$ | $\phantom{-}e^{2} + 12$ |
| 47 | $[47, 47, w - 7]$ | $-e^{2} - 12$ |
| 59 | $[59, 59, -w - 5]$ | $\phantom{-}e^{2} + 12$ |
| 59 | $[59, 59, w - 6]$ | $-e^{2} - 12$ |
| 61 | $[61, 61, w + 16]$ | $-\frac{1}{8}e^{3} - 4e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).