Base field 5.5.89417.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - x^{2} + 8x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[33, 33, w^{4} - w^{3} - 4w^{2} + 4w + 3]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{2} - 3]$ | $\phantom{-}1$ |
5 | $[5, 5, w^{4} - 5w^{2} + 4]$ | $-3$ |
11 | $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $\phantom{-}1$ |
17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $\phantom{-}1$ |
32 | $[32, 2, 2]$ | $\phantom{-}5$ |
37 | $[37, 37, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ | $-3$ |
37 | $[37, 37, -w^{3} + 4w - 1]$ | $\phantom{-}0$ |
41 | $[41, 41, w^{3} + w^{2} - 4w - 1]$ | $-10$ |
41 | $[41, 41, -w^{3} + 2w + 2]$ | $\phantom{-}2$ |
43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}12$ |
49 | $[49, 7, w^{4} - 5w^{2} + 2]$ | $-5$ |
53 | $[53, 53, w^{4} - w^{3} - 5w^{2} + 2w + 5]$ | $-12$ |
59 | $[59, 59, w^{4} - w^{3} - 4w^{2} + 3w - 1]$ | $-7$ |
67 | $[67, 67, -w^{4} + 3w^{2} + 2w + 2]$ | $-11$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 2]$ | $-10$ |
81 | $[81, 3, -w^{4} + 6w^{2} + w - 8]$ | $-13$ |
83 | $[83, 83, w^{4} + w^{3} - 5w^{2} - 4w + 1]$ | $\phantom{-}3$ |
89 | $[89, 89, -w^{4} + 5w^{2} + w - 1]$ | $-6$ |
97 | $[97, 97, -w^{4} + 2w^{3} + 5w^{2} - 5w - 5]$ | $\phantom{-}4$ |
101 | $[101, 101, 2w^{2} - w - 2]$ | $\phantom{-}10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w^{2} - 3]$ | $-1$ |
$11$ | $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $-1$ |