Base field 5.5.38569.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} + 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[77, 77, -w^{4} - w^{3} + 4w^{2} + 4w - 3]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, -w^{2} + 2]$ | $-1$ |
11 | $[11, 11, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}1$ |
11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}0$ |
13 | $[13, 13, w^{4} - 5w^{2} + 2]$ | $\phantom{-}6$ |
17 | $[17, 17, w^{3} - 3w - 1]$ | $\phantom{-}6$ |
32 | $[32, 2, 2]$ | $-11$ |
37 | $[37, 37, w^{4} + w^{3} - 5w^{2} - 5w + 4]$ | $-2$ |
43 | $[43, 43, w^{2} + w - 3]$ | $\phantom{-}4$ |
43 | $[43, 43, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-4$ |
47 | $[47, 47, -w^{4} - w^{3} + 6w^{2} + 4w - 5]$ | $-8$ |
59 | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $\phantom{-}4$ |
67 | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}8$ |
73 | $[73, 73, w^{4} - 3w^{2} - w - 1]$ | $\phantom{-}10$ |
73 | $[73, 73, -2w^{4} - w^{3} + 9w^{2} + 5w - 6]$ | $\phantom{-}6$ |
79 | $[79, 79, -3w^{4} + 13w^{2} + 2w - 7]$ | $-8$ |
79 | $[79, 79, -w^{3} + 5w]$ | $\phantom{-}8$ |
79 | $[79, 79, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}12$ |
83 | $[83, 83, -2w^{4} - 2w^{3} + 11w^{2} + 7w - 8]$ | $\phantom{-}12$ |
89 | $[89, 89, -w^{4} - 2w^{3} + 4w^{2} + 7w - 3]$ | $-14$ |
101 | $[101, 101, -w^{4} + 5w^{2} - w - 4]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w^{2} + 2]$ | $1$ |
$11$ | $[11, 11, -w^{3} + w^{2} + 4w - 2]$ | $-1$ |