Base field 4.4.2777.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + x + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[59, 59, 2w^{2} - w - 7]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
8 | $[8, 2, -w^{3} + w^{2} + 4w - 1]$ | $-1$ |
11 | $[11, 11, w^{3} - 2w^{2} - 2w + 1]$ | $-4$ |
23 | $[23, 23, -w^{3} + 4w + 1]$ | $\phantom{-}0$ |
23 | $[23, 23, -w^{2} + 2w + 3]$ | $-4$ |
31 | $[31, 31, w^{3} - 2w^{2} - w + 3]$ | $\phantom{-}4$ |
37 | $[37, 37, -w^{3} + 3w + 3]$ | $-10$ |
37 | $[37, 37, -2w^{3} + 3w^{2} + 6w - 3]$ | $-6$ |
41 | $[41, 41, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}6$ |
41 | $[41, 41, -2w^{3} + 2w^{2} + 6w - 1]$ | $\phantom{-}6$ |
43 | $[43, 43, -w^{2} + w + 5]$ | $-8$ |
47 | $[47, 47, 2w^{2} - 3w - 5]$ | $-4$ |
53 | $[53, 53, -w^{3} + 3w^{2} + w - 7]$ | $-2$ |
53 | $[53, 53, -2w^{2} + 2w + 5]$ | $-2$ |
59 | $[59, 59, 2w^{2} - w - 7]$ | $\phantom{-}1$ |
61 | $[61, 61, 2w^{2} - w - 3]$ | $-2$ |
61 | $[61, 61, 2w^{2} - w - 5]$ | $\phantom{-}10$ |
67 | $[67, 67, 2w^{3} - 2w^{2} - 7w + 3]$ | $\phantom{-}12$ |
67 | $[67, 67, 2w^{3} - 2w^{2} - 7w - 1]$ | $\phantom{-}4$ |
71 | $[71, 71, 2w^{3} - 4w^{2} - 4w + 7]$ | $-16$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59, 59, 2w^{2} - w - 7]$ | $-1$ |