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: | $[2, 2, w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 16x^{6} + 138x^{4} - 272x^{2} + 1369\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{504}e^{6} - \frac{5}{168}e^{4} - \frac{55}{168}e^{2} + \frac{101}{504}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{4}{3367}e^{7} + \frac{219}{13468}e^{5} + \frac{478}{3367}e^{3} + \frac{3011}{13468}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{113}{40404}e^{7} + \frac{363}{6734}e^{5} + \frac{7307}{13468}e^{3} + \frac{15157}{20202}e$ |
| 5 | $[5, 5, -2w + 15]$ | $\phantom{-}2$ |
| 11 | $[11, 11, 3w - 22]$ | $-\frac{4}{3367}e^{7} - \frac{219}{13468}e^{5} - \frac{478}{3367}e^{3} + \frac{10457}{13468}e$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{5}{546}e^{6} - \frac{57}{364}e^{4} - \frac{275}{182}e^{2} + \frac{905}{1092}$ |
| 13 | $[13, 13, w + 9]$ | $-\frac{1}{364}e^{6} - \frac{2}{91}e^{4} - \frac{165}{364}e^{2} + \frac{34}{91}$ |
| 17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{9}{728}e^{6} + \frac{163}{728}e^{4} + \frac{1485}{728}e^{2} - \frac{769}{728}$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{1}{2184}e^{6} - \frac{33}{728}e^{4} - \frac{55}{728}e^{2} - \frac{319}{2184}$ |
| 19 | $[19, 19, -w - 6]$ | $-\frac{29}{3848}e^{7} - \frac{427}{3848}e^{5} - \frac{3225}{3848}e^{3} + \frac{17841}{3848}e$ |
| 19 | $[19, 19, w - 6]$ | $-\frac{3}{3848}e^{7} - \frac{11}{3848}e^{5} - \frac{599}{3848}e^{3} + \frac{3073}{3848}e$ |
| 23 | $[23, 23, w + 3]$ | $-\frac{5}{1554}e^{7} - \frac{39}{518}e^{5} - \frac{415}{518}e^{3} - \frac{1637}{1554}e$ |
| 23 | $[23, 23, w + 20]$ | $\phantom{-}\frac{5}{1554}e^{7} + \frac{39}{518}e^{5} + \frac{415}{518}e^{3} + \frac{1637}{1554}e$ |
| 47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$ |
| 47 | $[47, 47, w + 33]$ | $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}3$ |
| 67 | $[67, 67, w + 16]$ | $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$ |
| 67 | $[67, 67, w + 51]$ | $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$ |
| 73 | $[73, 73, w + 36]$ | $-\frac{1}{182}e^{6} - \frac{4}{91}e^{4} - \frac{165}{182}e^{2} + \frac{68}{91}$ |
| 73 | $[73, 73, w + 37]$ | $-\frac{5}{273}e^{6} - \frac{57}{182}e^{4} - \frac{275}{91}e^{2} + \frac{905}{546}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $\frac{1}{504}e^{6} + \frac{5}{168}e^{4} + \frac{55}{168}e^{2} - \frac{101}{504}$ |