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: | $[3,3,-w + 1]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 60x^{14} + 1346x^{12} + 14040x^{10} + 67921x^{8} + 129884x^{6} + 74064x^{4} + 13504x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $...$ |
| 3 | $[3, 3, w + 1]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{11523}{1313824}e^{15} - \frac{686685}{1313824}e^{13} - \frac{951877}{82114}e^{11} - \frac{9723097}{82114}e^{9} - \frac{719100509}{1313824}e^{7} - \frac{1202061251}{1313824}e^{5} - \frac{11145560}{41057}e^{3} + \frac{59629}{41057}e$ |
| 5 | $[5, 5, -2w + 15]$ | $...$ |
| 11 | $[11, 11, 3w - 22]$ | $...$ |
| 13 | $[13, 13, w + 4]$ | $...$ |
| 13 | $[13, 13, w + 9]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 15]$ | $...$ |
| 19 | $[19, 19, -w - 6]$ | $...$ |
| 19 | $[19, 19, w - 6]$ | $...$ |
| 23 | $[23, 23, w + 3]$ | $...$ |
| 23 | $[23, 23, w + 20]$ | $...$ |
| 47 | $[47, 47, w + 14]$ | $...$ |
| 47 | $[47, 47, w + 33]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 67 | $[67, 67, w + 16]$ | $...$ |
| 67 | $[67, 67, w + 51]$ | $...$ |
| 73 | $[73, 73, w + 36]$ | $...$ |
| 73 | $[73, 73, w + 37]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $\frac{11523}{1313824}e^{15} + \frac{686685}{1313824}e^{13} + \frac{951877}{82114}e^{11} + \frac{9723097}{82114}e^{9} + \frac{719100509}{1313824}e^{7} + \frac{1202061251}{1313824}e^{5} + \frac{11145560}{41057}e^{3} - \frac{59629}{41057}e$ |