Base field \(\Q(\sqrt{14}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[11,11,-w + 5]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 4x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 4]$ | $\phantom{-}e^{2} - 1$ |
5 | $[5, 5, -w + 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}e^{3} - 5e$ |
7 | $[7, 7, -2w - 7]$ | $\phantom{-}2e^{3} - 7e$ |
9 | $[9, 3, 3]$ | $\phantom{-}0$ |
11 | $[11, 11, w + 5]$ | $\phantom{-}2$ |
11 | $[11, 11, -w + 5]$ | $-1$ |
13 | $[13, 13, -w - 1]$ | $\phantom{-}4e^{3} - 11e$ |
13 | $[13, 13, -w + 1]$ | $-3e^{3} + 10e$ |
31 | $[31, 31, 2w - 5]$ | $\phantom{-}2e$ |
31 | $[31, 31, -2w - 5]$ | $-e^{3} + e$ |
43 | $[43, 43, 7w + 27]$ | $\phantom{-}e^{2} + 2$ |
43 | $[43, 43, 3w + 13]$ | $-5e^{2} + 10$ |
47 | $[47, 47, 2w - 3]$ | $-2e^{3} + 10e$ |
47 | $[47, 47, -2w - 3]$ | $-4e^{3} + 15e$ |
61 | $[61, 61, 7w + 25]$ | $-5e^{3} + 13e$ |
61 | $[61, 61, -5w - 17]$ | $-7e^{3} + 18e$ |
67 | $[67, 67, -w - 9]$ | $\phantom{-}3e^{2} - 6$ |
67 | $[67, 67, w - 9]$ | $\phantom{-}2e^{2}$ |
101 | $[101, 101, 3w - 5]$ | $-3e^{3} + 4e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,-w + 5]$ | $1$ |