Base field \(\Q(\sqrt{97}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 24\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, -12w + 65]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - 2x^{16} - 24x^{15} + 49x^{14} + 224x^{13} - 471x^{12} - 1025x^{11} + 2241x^{10} + 2388x^{9} - 5470x^{8} - 2737x^{7} + 6398x^{6} + 1661x^{5} - 2972x^{4} - 778x^{3} + 316x^{2} + 70x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 7w - 38]$ | $...$ |
| 2 | $[2, 2, -7w - 31]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w + 9]$ | $...$ |
| 3 | $[3, 3, 2w - 11]$ | $...$ |
| 11 | $[11, 11, -12w + 65]$ | $-1$ |
| 11 | $[11, 11, -12w - 53]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, 8w - 43]$ | $...$ |
| 31 | $[31, 31, 8w + 35]$ | $...$ |
| 43 | $[43, 43, 54w + 239]$ | $...$ |
| 43 | $[43, 43, -54w + 293]$ | $...$ |
| 47 | $[47, 47, 2w - 13]$ | $...$ |
| 47 | $[47, 47, -2w - 11]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, 4w + 19]$ | $...$ |
| 53 | $[53, 53, 4w - 23]$ | $...$ |
| 61 | $[61, 61, 2w - 7]$ | $...$ |
| 61 | $[61, 61, -2w - 5]$ | $...$ |
| 73 | $[73, 73, 22w + 97]$ | $...$ |
| 73 | $[73, 73, -22w + 119]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -12w + 65]$ | $1$ |