Properties

Label 6.6.722000.1-49.2-a
Base field 6.6.722000.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49,7,w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 6.6.722000.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[49,7,w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $17$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{5} + 6w^{3} - w^{2} - 6w]$ $\phantom{-}2$
19 $[19, 19, 3w^{5} - 2w^{4} - 19w^{3} + 14w^{2} + 18w - 9]$ $\phantom{-}4$
29 $[29, 29, -w^{2} - w + 2]$ $\phantom{-}6$
29 $[29, 29, 2w^{5} - w^{4} - 13w^{3} + 7w^{2} + 14w - 3]$ $\phantom{-}6$
29 $[29, 29, -2w^{5} + w^{4} + 13w^{3} - 8w^{2} - 15w + 6]$ $-6$
49 $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ $\phantom{-}10$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$ $-1$
49 $[49, 7, w^{2} - 3]$ $\phantom{-}6$
59 $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ $\phantom{-}4$
59 $[59, 59, 2w^{5} - 12w^{3} + 3w^{2} + 12w - 3]$ $-4$
59 $[59, 59, -2w^{5} + w^{4} + 12w^{3} - 8w^{2} - 11w + 3]$ $\phantom{-}0$
61 $[61, 61, -4w^{5} + 2w^{4} + 24w^{3} - 16w^{2} - 19w + 8]$ $-10$
61 $[61, 61, 5w^{5} - 3w^{4} - 31w^{3} + 22w^{2} + 27w - 13]$ $\phantom{-}2$
61 $[61, 61, 3w^{5} - w^{4} - 18w^{3} + 9w^{2} + 16w - 4]$ $-14$
71 $[71, 71, 2w^{5} - 12w^{3} + 2w^{2} + 11w - 1]$ $\phantom{-}8$
71 $[71, 71, 3w^{5} - 2w^{4} - 18w^{3} + 15w^{2} + 13w - 9]$ $\phantom{-}16$
71 $[71, 71, -w^{5} + w^{4} + 6w^{3} - 7w^{2} - 6w + 5]$ $-8$
79 $[79, 79, -w^{5} + 7w^{3} - w^{2} - 10w]$ $-4$
79 $[79, 79, 4w^{5} - 2w^{4} - 25w^{3} + 15w^{2} + 23w - 9]$ $-16$
79 $[79, 79, -w^{5} + 6w^{3} - 2w^{2} - 7w + 4]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49,7,w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$ $1$