Base field 6.6.1541581.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $47$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}2$ |
11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $\phantom{-}0$ |
11 | $[11, 11, w^{2} - w - 2]$ | $\phantom{-}4$ |
17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $\phantom{-}2$ |
27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}8$ |
27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-8$ |
37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}6$ |
47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $-1$ |
53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $\phantom{-}6$ |
59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $\phantom{-}4$ |
64 | $[64, 2, -2]$ | $-3$ |
67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}8$ |
67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $\phantom{-}12$ |
71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}8$ |
71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}8$ |
73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $-10$ |
83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $-12$ |
83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $\phantom{-}4$ |
89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $-14$ |
97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$47$ | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $1$ |