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: | $[25, 5, 5]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 16x^{6} + 14x^{5} + 78x^{4} - 50x^{3} - 112x^{2} + 8x + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -2w - 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - 7e^{4} - 5e^{3} + 25e^{2} + 9e - 8$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{7} + 7e^{5} - \frac{1}{2}e^{4} - 26e^{3} + 5e^{2} + 14e - 2$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{13}{2}e^{4} - e^{3} + 21e^{2} + 6e - 6$ |
| 11 | $[11, 11, -w + 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{13}{2}e^{4} - e^{3} + 21e^{2} + 6e - 6$ |
| 13 | $[13, 13, -w - 1]$ | $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 22e^{2} + 10$ |
| 13 | $[13, 13, -w + 1]$ | $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 22e^{2} + 10$ |
| 31 | $[31, 31, 2w - 5]$ | $-e^{4} + e^{3} + 8e^{2} - 6e - 8$ |
| 31 | $[31, 31, -2w - 5]$ | $-e^{4} + e^{3} + 8e^{2} - 6e - 8$ |
| 43 | $[43, 43, 7w + 27]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{15}{2}e^{5} + e^{4} + 31e^{3} - 8e^{2} - 25e + 2$ |
| 43 | $[43, 43, 3w + 13]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{15}{2}e^{5} + e^{4} + 31e^{3} - 8e^{2} - 25e + 2$ |
| 47 | $[47, 47, 2w - 3]$ | $-\frac{1}{2}e^{7} - \frac{1}{2}e^{6} + \frac{13}{2}e^{5} + \frac{13}{2}e^{4} - 20e^{3} - 19e^{2} - 3e$ |
| 47 | $[47, 47, -2w - 3]$ | $-\frac{1}{2}e^{7} - \frac{1}{2}e^{6} + \frac{13}{2}e^{5} + \frac{13}{2}e^{4} - 20e^{3} - 19e^{2} - 3e$ |
| 61 | $[61, 61, 7w + 25]$ | $\phantom{-}e^{4} - e^{3} - 6e^{2} + 8e - 2$ |
| 61 | $[61, 61, -5w - 17]$ | $\phantom{-}e^{4} - e^{3} - 6e^{2} + 8e - 2$ |
| 67 | $[67, 67, -w - 9]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{13}{2}e^{5} + e^{4} + 20e^{3} - 10e^{2} + 3e + 14$ |
| 67 | $[67, 67, w - 9]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{13}{2}e^{5} + e^{4} + 20e^{3} - 10e^{2} + 3e + 14$ |
| 101 | $[101, 101, 3w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - 7e^{5} + 7e^{4} + 28e^{3} - 25e^{2} - 30e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w + 3]$ | $-1$ |
| $5$ | $[5, 5, w + 3]$ | $-1$ |