Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w + 3]$ |
| Dimension: | $32$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $132$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{32} - 223x^{30} + 22103x^{28} - 1290958x^{26} + 49663863x^{24} - 1331972743x^{22} + 25693150441x^{20} - 362213617944x^{18} + 3751432194448x^{16} - 28431019010496x^{14} + 155622102469920x^{12} - 600905590863552x^{10} + 1576742769637056x^{8} - 2650608897331968x^{6} + 2580874502079744x^{4} - 1180093682313216x^{2} + 126896439988224\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 17 | $[17, 17, w + 8]$ | $...$ |
| 23 | $[23, 23, w + 4]$ | $...$ |
| 23 | $[23, 23, w + 18]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, w + 1]$ | $...$ |
| 29 | $[29, 29, w + 27]$ | $...$ |
| 31 | $[31, 31, w + 13]$ | $...$ |
| 31 | $[31, 31, w + 17]$ | $...$ |
| 43 | $[43, 43, -w - 11]$ | $...$ |
| 43 | $[43, 43, w - 12]$ | $...$ |
| 47 | $[47, 47, -w - 6]$ | $...$ |
| 47 | $[47, 47, w - 7]$ | $...$ |
| 59 | $[59, 59, -w - 5]$ | $...$ |
| 59 | $[59, 59, w - 6]$ | $...$ |
| 61 | $[61, 61, w + 16]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 3]$ | $-1$ |