Base field 6.6.1292517.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 6x^{2} - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[53,53,-w^{5} - 2w^{4} + 6w^{3} + 12w^{2} - 3w - 7]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{5} + 6w^{3} + w^{2} - 5w - 1]$ | $-4$ |
17 | $[17, 17, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 5w + 1]$ | $-3$ |
17 | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ | $\phantom{-}4$ |
17 | $[17, 17, w^{4} - 5w^{2} - 2w + 1]$ | $-4$ |
17 | $[17, 17, -w^{5} - w^{4} + 5w^{3} + 7w^{2} - 3]$ | $-5$ |
19 | $[19, 19, 2w^{5} - 11w^{3} - 2w^{2} + 7w]$ | $\phantom{-}7$ |
19 | $[19, 19, w^{5} - 5w^{3} - w^{2} + 2w - 1]$ | $-4$ |
37 | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ | $-7$ |
37 | $[37, 37, -2w^{5} - w^{4} + 11w^{3} + 8w^{2} - 6w - 2]$ | $-8$ |
53 | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ | $\phantom{-}9$ |
53 | $[53, 53, w^{3} - 4w + 1]$ | $-1$ |
64 | $[64, 2, -2]$ | $-15$ |
73 | $[73, 73, -3w^{5} + 17w^{3} + 3w^{2} - 12w + 1]$ | $-2$ |
73 | $[73, 73, w^{3} - w^{2} - 4w + 1]$ | $-4$ |
73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 7w^{2} + 5w + 3]$ | $\phantom{-}7$ |
73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 8w^{2} + 5w + 4]$ | $-14$ |
107 | $[107, 107, -w^{4} + w^{3} + 5w^{2} - 2w - 3]$ | $-8$ |
107 | $[107, 107, -3w^{5} - w^{4} + 17w^{3} + 8w^{2} - 11w - 2]$ | $-8$ |
109 | $[109, 109, w^{4} - 6w^{2} + 5]$ | $\phantom{-}5$ |
109 | $[109, 109, -w^{5} + 6w^{3} + w^{2} - 7w + 1]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$53$ | $[53,53,-w^{5} - 2w^{4} + 6w^{3} + 12w^{2} - 3w - 7]$ | $1$ |