Base field 6.6.1683101.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w]$ | $-3$ |
7 | $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ | $\phantom{-}3$ |
13 | $[13, 13, w^{2} - 3]$ | $-1$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}5$ |
29 | $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ | $\phantom{-}4$ |
29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ | $\phantom{-}4$ |
41 | $[41, 41, -w^{2} + 4]$ | $\phantom{-}10$ |
41 | $[41, 41, -w^{2} + 2w + 3]$ | $-2$ |
43 | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $-1$ |
43 | $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $\phantom{-}4$ |
64 | $[64, 2, -2]$ | $\phantom{-}5$ |
71 | $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ | $\phantom{-}8$ |
71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ | $\phantom{-}8$ |
71 | $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-10$ |
71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ | $\phantom{-}8$ |
83 | $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ | $\phantom{-}5$ |
83 | $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ | $-7$ |
97 | $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $-2$ |
97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ | $\phantom{-}10$ |
113 | $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ | $-15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$43$ | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $1$ |