Base field 6.6.1279733.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ | $-1$ |
7 | $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ | $\phantom{-}0$ |
13 | $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ | $-2$ |
29 | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ | $-6$ |
29 | $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}10$ |
29 | $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ | $\phantom{-}2$ |
29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}10$ |
41 | $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ | $-6$ |
43 | $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ | $-4$ |
43 | $[43, 43, w^{3} - w^{2} - 2w + 1]$ | $\phantom{-}4$ |
64 | $[64, 2, -2]$ | $-7$ |
71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-8$ |
71 | $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ | $\phantom{-}8$ |
83 | $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ | $\phantom{-}12$ |
83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ | $\phantom{-}4$ |
83 | $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ | $\phantom{-}4$ |
83 | $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ | $\phantom{-}4$ |
97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ | $\phantom{-}14$ |
97 | $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ | $\phantom{-}14$ |
113 | $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ | $1$ |