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: | $[13,13,-3w + 22]$ |
| Dimension: | $30$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{30} - 8x^{29} - 31x^{28} + 388x^{27} + 162x^{26} - 8257x^{25} + 6477x^{24} + 101111x^{23} - 146177x^{22} - 784070x^{21} + 1510544x^{20} + 3980829x^{19} - 9481058x^{18} - 13117172x^{17} + 38882060x^{16} + 26141220x^{15} - 106099813x^{14} - 23027127x^{13} + 190556783x^{12} - 19474948x^{11} - 216732008x^{10} + 76444430x^{9} + 143094429x^{8} - 85338009x^{7} - 42859963x^{6} + 43218360x^{5} - 1444862x^{4} - 7916652x^{3} + 2692944x^{2} - 257344x - 4484\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $...$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 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 | $[13, 13, 3w - 22]$ | $-1$ |
| 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 |
|---|---|---|
| $13$ | $[13,13,-3w + 22]$ | $1$ |