Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[27, 9, 3w + 18]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 19x^{6} + 112x^{4} - 225x^{2} + 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w + 7]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -3w - 17]$ | $-\frac{2}{9}e^{6} + \frac{29}{9}e^{4} - \frac{98}{9}e^{2} + 5$ |
| 11 | $[11, 11, 3w - 20]$ | $\phantom{-}\frac{1}{27}e^{7} - \frac{10}{27}e^{5} - \frac{5}{27}e^{3} + 4e$ |
| 13 | $[13, 13, 2w - 13]$ | $-\frac{2}{9}e^{6} + \frac{29}{9}e^{4} - \frac{98}{9}e^{2} + 5$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}\frac{2}{9}e^{6} - \frac{29}{9}e^{4} + \frac{98}{9}e^{2} - 5$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{1}{9}e^{6} - \frac{19}{9}e^{4} + \frac{103}{9}e^{2} - 11$ |
| 17 | $[17, 17, -w + 8]$ | $-\frac{4}{27}e^{7} + \frac{67}{27}e^{5} - \frac{304}{27}e^{3} + 13e$ |
| 19 | $[19, 19, -w - 4]$ | $\phantom{-}\frac{1}{27}e^{7} - \frac{10}{27}e^{5} - \frac{32}{27}e^{3} + 11e$ |
| 19 | $[19, 19, -w + 5]$ | $-\frac{1}{9}e^{7} + \frac{16}{9}e^{5} - \frac{64}{9}e^{3} + \frac{11}{3}e$ |
| 25 | $[25, 5, 5]$ | $-\frac{1}{27}e^{7} + \frac{19}{27}e^{5} - \frac{112}{27}e^{3} + \frac{22}{3}e$ |
| 31 | $[31, 31, -6w - 35]$ | $-\frac{2}{9}e^{7} + \frac{32}{9}e^{5} - \frac{137}{9}e^{3} + \frac{55}{3}e$ |
| 31 | $[31, 31, -6w + 41]$ | $\phantom{-}e^{3} - 7e$ |
| 37 | $[37, 37, -w - 1]$ | $-\frac{1}{9}e^{7} + \frac{16}{9}e^{5} - \frac{64}{9}e^{3} + \frac{17}{3}e$ |
| 37 | $[37, 37, w - 2]$ | $\phantom{-}\frac{5}{27}e^{7} - \frac{86}{27}e^{5} + \frac{416}{27}e^{3} - \frac{61}{3}e$ |
| 47 | $[47, 47, 3w + 16]$ | $-\frac{5}{27}e^{7} + \frac{77}{27}e^{5} - \frac{299}{27}e^{3} + 9e$ |
| 47 | $[47, 47, -3w + 19]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{16}{3}e^{4} + \frac{61}{3}e^{2} - 12$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{9}e^{6} - \frac{19}{9}e^{4} + \frac{85}{9}e^{2} - 5$ |
| 67 | $[67, 67, 3w - 22]$ | $-e^{4} + 10e^{2} - 13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 6]$ | $1$ |
| $3$ | $[3, 3, -w + 7]$ | $1$ |