Base field \(\Q(\sqrt{55}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, 2w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 16x^{6} + 79x^{4} - 136x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-e$ |
| 5 | $[5, 5, -2w + 15]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 6$ |
| 11 | $[11, 11, 3w - 22]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + \frac{35}{4}e^{2} - 6$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + \frac{35}{4}e^{2} - 6$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{1}{4}e^{6} + \frac{7}{2}e^{4} - \frac{57}{4}e^{2} + 14$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{1}{4}e^{6} + \frac{7}{2}e^{4} - \frac{57}{4}e^{2} + 14$ |
| 19 | $[19, 19, -w - 6]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 12e$ |
| 19 | $[19, 19, w - 6]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 12e$ |
| 23 | $[23, 23, w + 3]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{7}{2}e^{5} + \frac{49}{4}e^{3} - 7e$ |
| 23 | $[23, 23, w + 20]$ | $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{49}{4}e^{3} + 7e$ |
| 47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{1}{4}e^{7} - 4e^{5} + \frac{75}{4}e^{3} - 25e$ |
| 47 | $[47, 47, w + 33]$ | $-\frac{1}{4}e^{7} + 4e^{5} - \frac{75}{4}e^{3} + 25e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}e^{6} - \frac{27}{2}e^{4} + \frac{95}{2}e^{2} - 42$ |
| 67 | $[67, 67, w + 16]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 11e$ |
| 67 | $[67, 67, w + 51]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 11e$ |
| 73 | $[73, 73, w + 36]$ | $-\frac{3}{4}e^{6} + 11e^{4} - \frac{177}{4}e^{2} + 38$ |
| 73 | $[73, 73, w + 37]$ | $-\frac{3}{4}e^{6} + 11e^{4} - \frac{177}{4}e^{2} + 38$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $-1$ |