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: | $[9, 3, 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 24x^{6} + 160x^{4} - 368x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 4]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{5}{4}e^{4} + 5e^{2} - 3$ |
| 5 | $[5, 5, -w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w - 7]$ | $-\frac{1}{8}e^{7} + \frac{11}{4}e^{5} - \frac{29}{2}e^{3} + 18e$ |
| 9 | $[9, 3, 3]$ | $-1$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{1}{8}e^{6} + \frac{11}{4}e^{4} - 15e^{2} + 20$ |
| 11 | $[11, 11, -w + 5]$ | $-\frac{1}{8}e^{6} + \frac{11}{4}e^{4} - 15e^{2} + 20$ |
| 13 | $[13, 13, -w - 1]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{3}{2}e^{5} + \frac{19}{2}e^{3} - 15e$ |
| 13 | $[13, 13, -w + 1]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{3}{2}e^{5} + \frac{19}{2}e^{3} - 15e$ |
| 31 | $[31, 31, 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e$ |
| 31 | $[31, 31, -2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e$ |
| 43 | $[43, 43, 7w + 27]$ | $-\frac{1}{8}e^{6} + \frac{5}{2}e^{4} - 11e^{2} + 12$ |
| 43 | $[43, 43, 3w + 13]$ | $-\frac{1}{8}e^{6} + \frac{5}{2}e^{4} - 11e^{2} + 12$ |
| 47 | $[47, 47, 2w - 3]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{5}{2}e^{5} + 10e^{3} - 4e$ |
| 47 | $[47, 47, -2w - 3]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{5}{2}e^{5} + 10e^{3} - 4e$ |
| 61 | $[61, 61, 7w + 25]$ | $\phantom{-}\frac{3}{16}e^{7} - 4e^{5} + \frac{39}{2}e^{3} - 19e$ |
| 61 | $[61, 61, -5w - 17]$ | $\phantom{-}\frac{3}{16}e^{7} - 4e^{5} + \frac{39}{2}e^{3} - 19e$ |
| 67 | $[67, 67, -w - 9]$ | $\phantom{-}\frac{3}{8}e^{6} - 8e^{4} + 39e^{2} - 44$ |
| 67 | $[67, 67, w - 9]$ | $\phantom{-}\frac{3}{8}e^{6} - 8e^{4} + 39e^{2} - 44$ |
| 101 | $[101, 101, 3w - 5]$ | $-3e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $1$ |