Base field \(\Q(\sqrt{15}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[17,17,-w + 7]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 9x^{4} + 24x^{2} - 19\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $-e^{4} + 7e^{2} - 9$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e^{2} - 1$ |
| 7 | $[7, 7, w + 1]$ | $-e^{3} + 3e$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}e^{5} - 6e^{3} + 7e$ |
| 11 | $[11, 11, -w - 2]$ | $-e^{3} + 4e$ |
| 11 | $[11, 11, w - 2]$ | $\phantom{-}2e^{5} - 14e^{3} + 21e$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}2e^{4} - 13e^{2} + 20$ |
| 17 | $[17, 17, w + 10]$ | $-1$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}e^{5} - 9e^{3} + 19e$ |
| 43 | $[43, 43, w + 31]$ | $-2e^{5} + 12e^{3} - 14e$ |
| 53 | $[53, 53, w + 11]$ | $-6e^{2} + 18$ |
| 53 | $[53, 53, w + 42]$ | $-2e^{4} + 16e^{2} - 20$ |
| 59 | $[59, 59, 2w - 1]$ | $-3e^{5} + 22e^{3} - 37e$ |
| 59 | $[59, 59, -2w - 1]$ | $-2e^{5} + 14e^{3} - 15e$ |
| 61 | $[61, 61, 2w - 11]$ | $-7e^{4} + 44e^{2} - 59$ |
| 61 | $[61, 61, -2w - 11]$ | $\phantom{-}4e^{4} - 26e^{2} + 36$ |
| 67 | $[67, 67, w + 22]$ | $-e^{5} + 7e^{3} - 16e$ |
| 67 | $[67, 67, w + 45]$ | $\phantom{-}3e^{5} - 22e^{3} + 33e$ |
| 71 | $[71, 71, 3w - 8]$ | $-2e^{5} + 16e^{3} - 29e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,-w + 7]$ | $1$ |