Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,-w + 2]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $150$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} + 30x^{18} + 573x^{16} + 6732x^{14} + 57919x^{12} + 334363x^{10} + 1394541x^{8} + 3383220x^{6} + 5741710x^{4} + 4288400x^{2} + 2280100\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $...$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $...$ |
| 13 | $[13, 13, w + 12]$ | $...$ |
| 43 | $[43, 43, -w - 6]$ | $...$ |
| 43 | $[43, 43, w - 6]$ | $...$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 28]$ | $...$ |
| 59 | $[59, 59, w + 16]$ | $...$ |
| 59 | $[59, 59, w + 43]$ | $...$ |
| 71 | $[71, 71, w + 24]$ | $...$ |
| 71 | $[71, 71, w + 47]$ | $...$ |
| 73 | $[73, 73, 3w - 28]$ | $...$ |
| 73 | $[73, 73, 12w - 107]$ | $...$ |
| 79 | $[79, 79, -w]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 2]$ | $\frac{3147404039871284}{7135800494916410033135}e^{18} + \frac{182658339001524613}{14271600989832820066270}e^{16} + \frac{1717985655031229237}{7135800494916410033135}e^{14} + \frac{7845521576415620921}{2854320197966564013254}e^{12} + \frac{165115221863597718589}{7135800494916410033135}e^{10} + \frac{1825087155888129905011}{14271600989832820066270}e^{8} + \frac{7357001927558015146537}{14271600989832820066270}e^{6} + \frac{15958397868033500742703}{14271600989832820066270}e^{4} + \frac{2923392583900626805247}{1427160098983282006627}e^{2} + \frac{4940585536930639903}{9451391383995245077}$ |