Base field \(\Q(\sqrt{67}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[14, 14, -w + 9]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} - 25x^{11} - 6x^{10} + 235x^{9} + 113x^{8} - 999x^{7} - 712x^{6} + 1729x^{5} + 1601x^{4} - 564x^{3} - 618x^{2} + 47x + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -27w + 221]$ | $-1$ |
| 3 | $[3, 3, -w + 8]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 8]$ | $...$ |
| 7 | $[7, 7, -11w + 90]$ | $...$ |
| 7 | $[7, 7, -11w - 90]$ | $\phantom{-}1$ |
| 11 | $[11, 11, 6w - 49]$ | $...$ |
| 11 | $[11, 11, 6w + 49]$ | $...$ |
| 17 | $[17, 17, 4w + 33]$ | $...$ |
| 17 | $[17, 17, -4w + 33]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, -70w + 573]$ | $...$ |
| 29 | $[29, 29, 151w - 1236]$ | $...$ |
| 31 | $[31, 31, -w - 6]$ | $...$ |
| 31 | $[31, 31, w - 6]$ | $...$ |
| 37 | $[37, 37, -21w - 172]$ | $...$ |
| 37 | $[37, 37, -21w + 172]$ | $...$ |
| 43 | $[43, 43, 2w - 15]$ | $...$ |
| 43 | $[43, 43, 2w + 15]$ | $...$ |
| 67 | $[67, 67, -w]$ | $...$ |
| 73 | $[73, 73, -3w - 26]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -27w + 221]$ | $1$ |
| $7$ | $[7, 7, -11w - 90]$ | $-1$ |