Properties

Label 6.6.1312625.1-41.1-i
Base field 6.6.1312625.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 6.6.1312625.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 7x^{3} + 12x^{2} - 12x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ $-1$
11 $[11, 11, w + 1]$ $-5$
16 $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ $\phantom{-}3$
19 $[19, 19, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}5$
29 $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ $\phantom{-}6$
31 $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ $-6$
41 $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ $\phantom{-}1$
41 $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ $\phantom{-}3$
59 $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ $-10$
61 $[61, 61, w^{5} - 7w^{3} + 10w]$ $\phantom{-}4$
61 $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ $-6$
71 $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ $\phantom{-}14$
71 $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ $-16$
71 $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ $-6$
79 $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ $\phantom{-}1$
79 $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ $-2$
79 $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ $-12$
89 $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ $-11$
89 $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ $-6$
89 $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ $-9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ $-1$