Base field 6.6.1683101.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[43,43,w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 7x + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w]$ | $-2$ |
7 | $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ | $-2$ |
13 | $[13, 13, w^{2} - 3]$ | $\phantom{-}e - 4$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}e$ |
29 | $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ | $-e + 9$ |
29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ | $\phantom{-}3e - 11$ |
41 | $[41, 41, -w^{2} + 4]$ | $-5e + 15$ |
41 | $[41, 41, -w^{2} + 2w + 3]$ | $-e + 7$ |
43 | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $\phantom{-}4e - 12$ |
43 | $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $\phantom{-}1$ |
64 | $[64, 2, -2]$ | $\phantom{-}6e - 19$ |
71 | $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ | $-2e$ |
71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ | $\phantom{-}2e - 8$ |
71 | $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-10e + 40$ |
71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ | $-2e + 4$ |
83 | $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ | $-6e + 16$ |
83 | $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ | $-6e + 16$ |
97 | $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $-11e + 32$ |
97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ | $\phantom{-}e - 4$ |
113 | $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ | $\phantom{-}9e - 33$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$43$ | $[43,43,w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 2]$ | $-1$ |