# Properties

 Label 6.6.1387029.1-49.1-h Base field 6.6.1387029.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $49$ Level $[49, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ Dimension $2$ CM no Base change yes

# Related objects

• L-function not available

## Base field 6.6.1387029.1

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

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[49, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ Dimension: $2$ CM: no Base change: yes Newspace dimension: $38$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{2} - 8$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ $\phantom{-}0$
25 $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ $-8$
37 $[37, 37, w^{3} - w^{2} - 4w + 2]$ $-\frac{3}{2}e$
37 $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ $-\frac{3}{2}e$
49 $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ $-\frac{3}{2}e$
49 $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ $-\frac{3}{2}e$
53 $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ $-\frac{9}{2}e$
53 $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-\frac{9}{2}e$
61 $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ $\phantom{-}8$
61 $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ $\phantom{-}\frac{9}{2}e$
61 $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ $\phantom{-}\frac{9}{2}e$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}8$
64 $[64, 2, -2]$ $-7$
67 $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ $-3e$
67 $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ $-3e$
71 $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ $-12$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $-12$
81 $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ $-16$
101 $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ $-\frac{9}{2}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ $-1$