Base field \(\Q(\sqrt{105}) \)
Generator \(w\), with minimal polynomial \(x^2 - x - 26\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6, 6, -w + 5]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{2} e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{2} e$ |
| 5 | $[5, 5, 2 w - 11]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{3}{2} e$ |
| 13 | $[13, 13, w]$ | $-\frac{1}{2} e$ |
| 13 | $[13, 13, w + 12]$ | $-3 e$ |
| 23 | $[23, 23, w + 8]$ | $-3 e$ |
| 23 | $[23, 23, w + 14]$ | $-\frac{1}{2} e$ |
| 41 | $[41, 41, 2 w - 9]$ | $\phantom{-}12$ |
| 41 | $[41, 41, -2 w - 7]$ | $\phantom{-}7$ |
| 53 | $[53, 53, w + 11]$ | $\phantom{-}\frac{9}{2} e$ |
| 53 | $[53, 53, w + 41]$ | $-\frac{11}{2} e$ |
| 59 | $[59, 59, 4 w + 17]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 4 w - 21]$ | $\phantom{-}0$ |
| 73 | $[73, 73, w + 27]$ | $-8 e$ |
| 73 | $[73, 73, w + 45]$ | $\phantom{-}7 e$ |
| 79 | $[79, 79, -6 w - 29]$ | $-10$ |
| 79 | $[79, 79, 6 w - 35]$ | $\phantom{-}10$ |
| 89 | $[89, 89, 2 w - 5]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $\frac{1}{2} e$ |
| $3$ | $[3, 3, w + 1]$ | $-\frac{1}{2} e$ |