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: | $[16, 4, 4]$ |
| Dimension: | $26$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{26} + 6x^{25} - 29x^{24} - 228x^{23} + 270x^{22} + 3671x^{21} + 30x^{20} - 32799x^{19} - 19125x^{18} + 179058x^{17} + 162461x^{16} - 620229x^{15} - 682982x^{14} + 1370526x^{13} + 1663030x^{12} - 1891314x^{11} - 2390939x^{10} + 1548898x^{9} + 1948871x^{8} - 689962x^{7} - 820572x^{6} + 146230x^{5} + 156861x^{4} - 5587x^{3} - 10834x^{2} - 1133x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $...$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, 4w + 25]$ | $...$ |
| 5 | $[5, 5, -4w + 29]$ | $...$ |
| 11 | $[11, 11, w - 8]$ | $...$ |
| 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 |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |