Base field 3.3.1620.1
Generator \(w\), with minimal polynomial \(x^{3} - 12x - 14\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[7, 7, -w^{2} + 2w + 7]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e - 2$ |
5 | $[5, 5, -w - 3]$ | $-e + 2$ |
5 | $[5, 5, -2w^{2} + 3w + 19]$ | $-2e + 2$ |
7 | $[7, 7, -w^{2} + 2w + 7]$ | $\phantom{-}1$ |
13 | $[13, 13, w^{2} - 3w - 5]$ | $\phantom{-}2e$ |
17 | $[17, 17, w^{2} - w - 3]$ | $\phantom{-}4$ |
23 | $[23, 23, -w + 3]$ | $\phantom{-}e + 2$ |
37 | $[37, 37, 3w + 5]$ | $-3e + 2$ |
43 | $[43, 43, w^{2} + 3w + 3]$ | $\phantom{-}2e$ |
47 | $[47, 47, -w^{2} + 3]$ | $\phantom{-}4e$ |
49 | $[49, 7, -w^{2} + 5]$ | $-e + 2$ |
53 | $[53, 53, -w^{2} + w + 13]$ | $\phantom{-}e + 2$ |
61 | $[61, 61, -w^{2} + 15]$ | $-2e$ |
61 | $[61, 61, w^{2} - 2w - 13]$ | $\phantom{-}2e - 10$ |
61 | $[61, 61, -4w - 5]$ | $-8$ |
67 | $[67, 67, -2w^{2} + 6w + 13]$ | $-7e + 6$ |
73 | $[73, 73, 2w^{2} - 2w - 17]$ | $\phantom{-}3e - 2$ |
79 | $[79, 79, -w - 5]$ | $\phantom{-}4e + 4$ |
79 | $[79, 79, 2w^{2} - 4w - 17]$ | $-5e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w^{2} + 2w + 7]$ | $-1$ |