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: | $[7, 7, 3w - 19]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 17x^{4} + 71x^{2} - 80\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $-e$ |
| 3 | $[3, 3, -w - 5]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{5}e^{4} + \frac{16}{5}e^{2} - 7$ |
| 7 | $[7, 7, 3w - 19]$ | $-1$ |
| 11 | $[11, 11, -2w - 11]$ | $-\frac{2}{5}e^{4} + \frac{27}{5}e^{2} - 12$ |
| 11 | $[11, 11, -2w + 13]$ | $-\frac{2}{5}e^{4} + \frac{27}{5}e^{2} - 12$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{1}{10}e^{5} + \frac{11}{10}e^{3} + \frac{1}{2}e$ |
| 13 | $[13, 13, -w + 5]$ | $\phantom{-}\frac{1}{10}e^{5} - \frac{11}{10}e^{3} - \frac{1}{2}e$ |
| 19 | $[19, 19, 5w - 31]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w - 7]$ | $-\frac{1}{5}e^{4} + \frac{11}{5}e^{2}$ |
| 23 | $[23, 23, w - 8]$ | $-\frac{1}{5}e^{4} + \frac{11}{5}e^{2}$ |
| 25 | $[25, 5, -5]$ | $-\frac{3}{5}e^{4} + \frac{43}{5}e^{2} - 22$ |
| 31 | $[31, 31, -w - 1]$ | $-\frac{2}{5}e^{5} + \frac{27}{5}e^{3} - 11e$ |
| 31 | $[31, 31, w - 2]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{27}{5}e^{3} + 11e$ |
| 41 | $[41, 41, 6w + 31]$ | $\phantom{-}\frac{7}{10}e^{5} - \frac{97}{10}e^{3} + \frac{43}{2}e$ |
| 41 | $[41, 41, 6w - 37]$ | $-\frac{7}{10}e^{5} + \frac{97}{10}e^{3} - \frac{43}{2}e$ |
| 43 | $[43, 43, -3w - 17]$ | $\phantom{-}\frac{4}{5}e^{4} - \frac{54}{5}e^{2} + 28$ |
| 43 | $[43, 43, -3w + 20]$ | $\phantom{-}\frac{4}{5}e^{4} - \frac{54}{5}e^{2} + 28$ |
| 59 | $[59, 59, 3w - 17]$ | $-\frac{4}{5}e^{5} + \frac{59}{5}e^{3} - 28e$ |
| 59 | $[59, 59, 3w + 14]$ | $\phantom{-}\frac{4}{5}e^{5} - \frac{59}{5}e^{3} + 28e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, 3w - 19]$ | $1$ |