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: | $[15, 15, w + 7]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $-1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, 2w - 11]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w]$ | $\phantom{-}2$ |
| 13 | $[13, 13, w + 12]$ | $\phantom{-}2$ |
| 23 | $[23, 23, w + 8]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 14]$ | $\phantom{-}0$ |
| 41 | $[41, 41, 2w - 9]$ | $-10$ |
| 41 | $[41, 41, -2w - 7]$ | $-10$ |
| 53 | $[53, 53, w + 11]$ | $-10$ |
| 53 | $[53, 53, w + 41]$ | $-10$ |
| 59 | $[59, 59, 4w + 17]$ | $\phantom{-}4$ |
| 59 | $[59, 59, 4w - 21]$ | $\phantom{-}4$ |
| 73 | $[73, 73, w + 27]$ | $-10$ |
| 73 | $[73, 73, w + 45]$ | $-10$ |
| 79 | $[79, 79, -6w - 29]$ | $\phantom{-}0$ |
| 79 | $[79, 79, 6w - 35]$ | $\phantom{-}0$ |
| 89 | $[89, 89, 2w - 5]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |
| $5$ | $[5, 5, 2w - 11]$ | $1$ |