Base field 3.3.892.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 10\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[10, 10, w]$ |
Dimension: | $2$ |
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:
\(x^{2} - 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}1$ |
2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{2} - w + 5]$ | $-1$ |
7 | $[7, 7, w^{2} + w - 9]$ | $-e + 1$ |
13 | $[13, 13, -w^{2} - w + 7]$ | $\phantom{-}2e - 4$ |
19 | $[19, 19, w^{2} - w - 1]$ | $-e + 3$ |
25 | $[25, 5, -w^{2} + w + 3]$ | $-2e + 6$ |
27 | $[27, 3, 3]$ | $\phantom{-}2e + 2$ |
31 | $[31, 31, -w^{2} + w + 11]$ | $\phantom{-}e - 1$ |
43 | $[43, 43, -3w^{2} - w + 21]$ | $\phantom{-}e - 1$ |
47 | $[47, 47, 2w - 1]$ | $\phantom{-}e + 3$ |
49 | $[49, 7, 4w^{2} + 2w - 29]$ | $-6e + 6$ |
61 | $[61, 61, 2w^{2} + 2w - 9]$ | $\phantom{-}6$ |
71 | $[71, 71, w^{2} + w - 11]$ | $-3e + 5$ |
71 | $[71, 71, -w^{2} - 3w + 7]$ | $\phantom{-}5e - 13$ |
71 | $[71, 71, 2w^{2} + 2w - 13]$ | $\phantom{-}6e - 4$ |
79 | $[79, 79, w^{2} + 3w - 1]$ | $-3e + 5$ |
79 | $[79, 79, w^{2} + w - 1]$ | $-3e + 15$ |
79 | $[79, 79, -w^{2} - 3w - 1]$ | $-2e + 12$ |
83 | $[83, 83, w^{2} - w - 7]$ | $\phantom{-}3e - 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 2]$ | $-1$ |
$5$ | $[5, 5, -w^{2} - w + 5]$ | $1$ |