Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,8,211w + 1663]$ |
| Dimension: | $21$ |
| 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:
| \(x^{21} + 3x^{20} - 29x^{19} - 89x^{18} + 349x^{17} + 1103x^{16} - 2258x^{15} - 7420x^{14} + 8491x^{13} + 29429x^{12} - 18705x^{11} - 69820x^{10} + 23269x^{9} + 95737x^{8} - 15823x^{7} - 69221x^{6} + 7480x^{5} + 21990x^{4} - 3145x^{3} - 1942x^{2} + 150x + 50\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -76w + 675]$ | $...$ |
| 5 | $[5, 5, 76w + 599]$ | $...$ |
| 7 | $[7, 7, -8w - 63]$ | $...$ |
| 7 | $[7, 7, -8w + 71]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 17 | $[17, 17, 42w + 331]$ | $...$ |
| 17 | $[17, 17, 42w - 373]$ | $...$ |
| 29 | $[29, 29, -6w - 47]$ | $...$ |
| 29 | $[29, 29, 6w - 53]$ | $...$ |
| 31 | $[31, 31, 10w + 79]$ | $...$ |
| 31 | $[31, 31, -10w + 89]$ | $...$ |
| 43 | $[43, 43, 2w - 19]$ | $...$ |
| 43 | $[43, 43, -2w - 17]$ | $...$ |
| 53 | $[53, 53, 194w + 1529]$ | $...$ |
| 53 | $[53, 53, -194w + 1723]$ | $...$ |
| 59 | $[59, 59, -110w - 867]$ | $...$ |
| 59 | $[59, 59, 110w - 977]$ | $...$ |
| 79 | $[79, 79, 650w - 5773]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 9]$ | $1$ |