Base field \(\Q(\sqrt{14}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[25, 25, -2w + 9]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 22x^{2} + 76\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 4]$ | $\phantom{-}\frac{1}{6}e^{2} - \frac{4}{3}$ |
| 5 | $[5, 5, -w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -2w - 7]$ | $-\frac{1}{6}e^{3} + \frac{7}{3}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{11}{3}$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}$ |
| 11 | $[11, 11, -w + 5]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{20}{3}$ |
| 13 | $[13, 13, -w - 1]$ | $-\frac{1}{6}e^{3} + \frac{10}{3}e$ |
| 13 | $[13, 13, -w + 1]$ | $-\frac{1}{6}e^{3} + \frac{10}{3}e$ |
| 31 | $[31, 31, 2w - 5]$ | $-\frac{1}{6}e^{3} + \frac{4}{3}e$ |
| 31 | $[31, 31, -2w - 5]$ | $-\frac{1}{6}e^{3} + \frac{4}{3}e$ |
| 43 | $[43, 43, 7w + 27]$ | $\phantom{-}9$ |
| 43 | $[43, 43, 3w + 13]$ | $-1$ |
| 47 | $[47, 47, 2w - 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e$ |
| 47 | $[47, 47, -2w - 3]$ | $-\frac{1}{2}e^{3} + 6e$ |
| 61 | $[61, 61, 7w + 25]$ | $-\frac{2}{3}e^{3} + \frac{28}{3}e$ |
| 61 | $[61, 61, -5w - 17]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{7}{3}e$ |
| 67 | $[67, 67, -w - 9]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{43}{3}$ |
| 67 | $[67, 67, w - 9]$ | $-e^{2} + 14$ |
| 101 | $[101, 101, 3w - 5]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{5}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 3]$ | $1$ |