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: | $[5, 5, -2w + 15]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 26x^{6} + 157x^{4} + 264x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{396}e^{7} + \frac{19}{198}e^{5} + \frac{415}{396}e^{3} + \frac{181}{66}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{396}e^{7} - \frac{19}{198}e^{5} - \frac{415}{396}e^{3} - \frac{115}{66}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{1}{396}e^{7} - \frac{19}{198}e^{5} - \frac{415}{396}e^{3} - \frac{115}{66}e$ |
| 5 | $[5, 5, -2w + 15]$ | $-1$ |
| 11 | $[11, 11, 3w - 22]$ | $-\frac{2}{33}e^{6} - \frac{43}{33}e^{4} - \frac{137}{33}e^{2} - \frac{20}{11}$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{1}{198}e^{7} - \frac{19}{99}e^{5} - \frac{415}{198}e^{3} - \frac{181}{33}e$ |
| 13 | $[13, 13, w + 9]$ | $-\frac{1}{198}e^{7} - \frac{19}{99}e^{5} - \frac{415}{198}e^{3} - \frac{181}{33}e$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{17}{396}e^{7} - \frac{112}{99}e^{5} - \frac{2897}{396}e^{3} - \frac{1031}{66}e$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{17}{396}e^{7} - \frac{112}{99}e^{5} - \frac{2897}{396}e^{3} - \frac{1031}{66}e$ |
| 19 | $[19, 19, -w - 6]$ | $\phantom{-}\frac{3}{22}e^{6} + \frac{35}{11}e^{4} + \frac{299}{22}e^{2} + \frac{100}{11}$ |
| 19 | $[19, 19, w - 6]$ | $\phantom{-}\frac{3}{22}e^{6} + \frac{35}{11}e^{4} + \frac{299}{22}e^{2} + \frac{100}{11}$ |
| 23 | $[23, 23, w + 3]$ | $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$ |
| 23 | $[23, 23, w + 20]$ | $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$ |
| 47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$ |
| 47 | $[47, 47, w + 33]$ | $\phantom{-}\frac{23}{198}e^{7} + \frac{577}{198}e^{5} + \frac{1555}{99}e^{3} + \frac{632}{33}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{2}{33}e^{6} + \frac{43}{33}e^{4} + \frac{104}{33}e^{2} - \frac{145}{11}$ |
| 67 | $[67, 67, w + 16]$ | $-\frac{4}{33}e^{7} - \frac{205}{66}e^{5} - \frac{1175}{66}e^{3} - \frac{249}{11}e$ |
| 67 | $[67, 67, w + 51]$ | $-\frac{4}{33}e^{7} - \frac{205}{66}e^{5} - \frac{1175}{66}e^{3} - \frac{249}{11}e$ |
| 73 | $[73, 73, w + 36]$ | $\phantom{-}\frac{1}{198}e^{7} + \frac{19}{99}e^{5} + \frac{415}{198}e^{3} + \frac{181}{33}e$ |
| 73 | $[73, 73, w + 37]$ | $\phantom{-}\frac{1}{198}e^{7} + \frac{19}{99}e^{5} + \frac{415}{198}e^{3} + \frac{181}{33}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -2w + 15]$ | $1$ |