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: | $[11, 11, -2w - 11]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 11x^{6} + 38x^{4} - 44x^{2} + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 5]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{10}{3}e^{5} + \frac{28}{3}e^{3} - \frac{19}{3}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{7}{3}e^{4} + \frac{7}{3}e^{2} + \frac{5}{3}$ |
| 7 | $[7, 7, 3w - 19]$ | $\phantom{-}e^{2} - 3$ |
| 11 | $[11, 11, -2w - 11]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -2w + 13]$ | $-\frac{1}{3}e^{6} + \frac{10}{3}e^{4} - \frac{25}{3}e^{2} + \frac{1}{3}$ |
| 13 | $[13, 13, w + 4]$ | $-e^{7} + 9e^{5} - 22e^{3} + 14e$ |
| 13 | $[13, 13, -w + 5]$ | $-\frac{1}{3}e^{7} + \frac{7}{3}e^{5} - \frac{4}{3}e^{3} - \frac{26}{3}e$ |
| 19 | $[19, 19, 5w - 31]$ | $-2e^{3} + 9e$ |
| 23 | $[23, 23, -w - 7]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{10}{3}e^{4} + \frac{25}{3}e^{2} - \frac{19}{3}$ |
| 23 | $[23, 23, w - 8]$ | $\phantom{-}3$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{7}{3}e^{4} + \frac{4}{3}e^{2} + \frac{8}{3}$ |
| 31 | $[31, 31, -w - 1]$ | $\phantom{-}\frac{4}{3}e^{7} - \frac{31}{3}e^{5} + \frac{46}{3}e^{3} + \frac{23}{3}e$ |
| 31 | $[31, 31, w - 2]$ | $-2e^{7} + 19e^{5} - 50e^{3} + 33e$ |
| 41 | $[41, 41, 6w + 31]$ | $\phantom{-}e^{5} - 7e^{3} + 12e$ |
| 41 | $[41, 41, 6w - 37]$ | $\phantom{-}\frac{2}{3}e^{7} - \frac{20}{3}e^{5} + \frac{65}{3}e^{3} - \frac{80}{3}e$ |
| 43 | $[43, 43, -3w - 17]$ | $-e^{4} + 6e^{2} - 8$ |
| 43 | $[43, 43, -3w + 20]$ | $-e^{6} + 6e^{4} - 3e^{2} - 8$ |
| 59 | $[59, 59, 3w - 17]$ | $\phantom{-}2e^{7} - 18e^{5} + 42e^{3} - 20e$ |
| 59 | $[59, 59, 3w + 14]$ | $-\frac{2}{3}e^{7} + \frac{20}{3}e^{5} - \frac{50}{3}e^{3} + \frac{11}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -2w - 11]$ | $-1$ |