Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[16, 4, 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 18x^{6} + 102x^{4} - 180x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 5]$ | $-\frac{1}{6}e^{5} + 2e^{3} - 6e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 3w - 19]$ | $\phantom{-}\frac{1}{6}e^{6} - 2e^{4} + 6e^{2} - 3$ |
| 11 | $[11, 11, -2w - 11]$ | $\phantom{-}\frac{1}{3}e^{6} - 4e^{4} + 11e^{2} - 1$ |
| 11 | $[11, 11, -2w + 13]$ | $\phantom{-}\frac{1}{6}e^{6} - 2e^{4} + 7e^{2} - 7$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{1}{6}e^{7} + \frac{13}{6}e^{5} - 8e^{3} + 9e$ |
| 13 | $[13, 13, -w + 5]$ | $\phantom{-}\frac{1}{6}e^{7} - \frac{5}{2}e^{5} + 11e^{3} - 13e$ |
| 19 | $[19, 19, 5w - 31]$ | $-\frac{2}{3}e^{5} + 6e^{3} - 8e$ |
| 23 | $[23, 23, -w - 7]$ | $-e^{2} + 8$ |
| 23 | $[23, 23, w - 8]$ | $-\frac{1}{6}e^{6} + 2e^{4} - 5e^{2} + 2$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{6}e^{6} - 2e^{4} + 6e^{2} - 3$ |
| 31 | $[31, 31, -w - 1]$ | $-\frac{1}{2}e^{5} + 5e^{3} - 8e$ |
| 31 | $[31, 31, w - 2]$ | $-\frac{2}{3}e^{5} + 7e^{3} - 15e$ |
| 41 | $[41, 41, 6w + 31]$ | $-\frac{1}{6}e^{7} + \frac{17}{6}e^{5} - 14e^{3} + 18e$ |
| 41 | $[41, 41, 6w - 37]$ | $\phantom{-}\frac{1}{6}e^{7} - 2e^{5} + 7e^{3} - 11e$ |
| 43 | $[43, 43, -3w - 17]$ | $\phantom{-}\frac{1}{3}e^{6} - 4e^{4} + 13e^{2} - 7$ |
| 43 | $[43, 43, -3w + 20]$ | $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + 17e^{2} - 1$ |
| 59 | $[59, 59, 3w - 17]$ | $-\frac{4}{3}e^{5} + 14e^{3} - 32e$ |
| 59 | $[59, 59, 3w + 14]$ | $-\frac{2}{3}e^{5} + 6e^{3} - 4e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |