Base field \(\Q(\zeta_{21})^+\)
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 8x^{2} - 8x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[43,43,w^{4} - 3w^{2} - 1]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 10x + 18\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, -w^{5} + 5w^{3} - 5w - 1]$ | $\phantom{-}4$ |
27 | $[27, 3, -2w^{5} + 10w^{3} - w^{2} - 10w + 2]$ | $\phantom{-}e$ |
41 | $[41, 41, -w^{5} + 6w^{3} - w^{2} - 7w + 2]$ | $-e$ |
41 | $[41, 41, w^{4} - w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}2e + 12$ |
41 | $[41, 41, -2w^{5} + 12w^{3} - 2w^{2} - 17w + 5]$ | $-2e - 12$ |
41 | $[41, 41, w^{5} - 5w^{3} + 2w^{2} + 5w - 5]$ | $-e$ |
41 | $[41, 41, -w^{4} - 2w^{3} + 4w^{2} + 6w - 3]$ | $-12$ |
41 | $[41, 41, -2w^{5} + 10w^{3} - w^{2} - 10w + 3]$ | $-2e - 12$ |
43 | $[43, 43, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 9w + 4]$ | $-4e - 20$ |
43 | $[43, 43, -w^{4} - w^{3} + 4w^{2} + 4w - 3]$ | $\phantom{-}2e + 10$ |
43 | $[43, 43, -w^{4} + 3w^{2} + 1]$ | $-1$ |
43 | $[43, 43, -w^{3} + w^{2} + 4w - 2]$ | $-4e - 20$ |
43 | $[43, 43, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 3]$ | $\phantom{-}2e + 10$ |
43 | $[43, 43, -w^{2} - w + 3]$ | $\phantom{-}4$ |
64 | $[64, 2, -2]$ | $-2e - 11$ |
83 | $[83, 83, -w^{5} + 6w^{3} - w^{2} - 10w + 4]$ | $\phantom{-}e + 12$ |
83 | $[83, 83, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 17w + 6]$ | $\phantom{-}5e + 24$ |
83 | $[83, 83, w^{5} - 6w^{3} + 2w^{2} + 8w - 3]$ | $\phantom{-}4e + 24$ |
83 | $[83, 83, w^{5} - 4w^{3} + w - 1]$ | $-2e$ |
83 | $[83, 83, -2w^{5} + 11w^{3} - w^{2} - 13w + 1]$ | $-4e - 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$43$ | $[43,43,w^{4} - 3w^{2} - 1]$ | $1$ |