Properties

Label 6.6.1416125.1-55.1-b
Base field 6.6.1416125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $55$
Level $[55, 55, -w^{3} + 2w + 1]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 6.6.1416125.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[55, 55, -w^{3} + 2w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $41$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ $\phantom{-}1$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $-1$
19 $[19, 19, -w^{3} + 4w]$ $-4$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ $-1$
19 $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ $\phantom{-}5$
25 $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ $-7$
29 $[29, 29, -w^{3} + 4w + 1]$ $\phantom{-}0$
41 $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $\phantom{-}0$
49 $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ $-10$
59 $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ $\phantom{-}3$
59 $[59, 59, -w^{3} + w^{2} + 2w - 3]$ $\phantom{-}12$
61 $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ $-4$
64 $[64, 2, -2]$ $-7$
71 $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ $\phantom{-}12$
71 $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ $-6$
79 $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ $-10$
79 $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ $\phantom{-}8$
89 $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ $-6$
109 $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ $-7$
109 $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ $-1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ $-1$
$11$ $[11, 11, w^{3} - w^{2} - 4w + 2]$ $1$