Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, w - 8]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} + 4x^{19} - 31x^{18} - 126x^{17} + 408x^{16} + 1632x^{15} - 3054x^{14} - 11215x^{13} + 14724x^{12} + 43767x^{11} - 47868x^{10} - 95072x^{9} + 100211x^{8} + 101310x^{7} - 114104x^{6} - 36096x^{5} + 47770x^{4} + 5651x^{3} - 7990x^{2} - 352x + 457\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, 4w + 25]$ | $...$ |
| 5 | $[5, 5, -4w + 29]$ | $...$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w - 7]$ | $...$ |
| 13 | $[13, 13, 3w + 19]$ | $...$ |
| 13 | $[13, 13, 3w - 22]$ | $...$ |
| 29 | $[29, 29, 6w + 37]$ | $...$ |
| 29 | $[29, 29, 6w - 43]$ | $...$ |
| 37 | $[37, 37, 2w - 13]$ | $...$ |
| 37 | $[37, 37, 2w + 11]$ | $...$ |
| 43 | $[43, 43, -w - 1]$ | $...$ |
| 43 | $[43, 43, w - 2]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 59 | $[59, 59, 5w - 37]$ | $...$ |
| 59 | $[59, 59, 5w + 32]$ | $...$ |
| 67 | $[67, 67, 21w + 131]$ | $...$ |
| 67 | $[67, 67, 21w - 152]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w - 8]$ | $-1$ |