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: | $4$ |
| 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:
| \(x^{4} - 13x^{2} + 27\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -3w - 17]$ | $-e^{2} + 6$ |
| 11 | $[11, 11, 3w - 20]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{13}{3}e$ |
| 13 | $[13, 13, 2w - 13]$ | $-e^{2} + 4$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}e^{2} - 8$ |
| 17 | $[17, 17, w + 7]$ | $-3$ |
| 17 | $[17, 17, -w + 8]$ | $-\frac{1}{3}e^{3} + \frac{16}{3}e$ |
| 19 | $[19, 19, -w - 4]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w + 5]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{20}{3}e$ |
| 25 | $[25, 5, 5]$ | $-e^{3} + 8e$ |
| 31 | $[31, 31, -6w - 35]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{19}{3}e$ |
| 31 | $[31, 31, -6w + 41]$ | $-\frac{1}{3}e^{3} + \frac{7}{3}e$ |
| 37 | $[37, 37, -w - 1]$ | $-\frac{2}{3}e^{3} + \frac{14}{3}e$ |
| 37 | $[37, 37, w - 2]$ | $\phantom{-}2e$ |
| 47 | $[47, 47, 3w + 16]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{23}{3}e$ |
| 47 | $[47, 47, -3w + 19]$ | $\phantom{-}3e^{2} - 21$ |
| 49 | $[49, 7, -7]$ | $-7$ |
| 67 | $[67, 67, 3w - 22]$ | $\phantom{-}e^{2} - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 6]$ | $1$ |
| $3$ | $[3, 3, -w + 7]$ | $-1$ |