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: | $[11,11,w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 5x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $-e^{3} - 5e$ |
5 | $[5, 5, w]$ | $\phantom{-}e^{3} + 3e$ |
7 | $[7, 7, w + 1]$ | $-2e$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}e^{3} + 5e$ |
11 | $[11, 11, -w - 2]$ | $\phantom{-}4$ |
11 | $[11, 11, w - 2]$ | $-1$ |
17 | $[17, 17, w + 7]$ | $\phantom{-}3e^{3} + 13e$ |
17 | $[17, 17, w + 10]$ | $-2e^{3} - 6e$ |
43 | $[43, 43, w + 12]$ | $-6e$ |
43 | $[43, 43, w + 31]$ | $\phantom{-}e^{3} + e$ |
53 | $[53, 53, w + 11]$ | $-4e^{3} - 16e$ |
53 | $[53, 53, w + 42]$ | $-4e^{3} - 16e$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}2e^{2} + 2$ |
59 | $[59, 59, -2w - 1]$ | $-2e^{2} - 10$ |
61 | $[61, 61, 2w - 11]$ | $-2$ |
61 | $[61, 61, -2w - 11]$ | $-4e^{2} - 14$ |
67 | $[67, 67, w + 22]$ | $-2e^{3} - 12e$ |
67 | $[67, 67, w + 45]$ | $\phantom{-}2e^{3} + 16e$ |
71 | $[71, 71, 3w - 8]$ | $-8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,w - 2]$ | $1$ |