# Properties

 Label 2.2.44.1-392.1-d Base field $$\Q(\sqrt{11})$$ Weight $[2, 2]$ Level norm $392$ Level $[392, 28, -14w + 42]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{11})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[392, 28, -14w + 42]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $56$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 3]$ $\phantom{-}0$
5 $[5, 5, w - 4]$ $-4$
5 $[5, 5, -w - 4]$ $-4$
7 $[7, 7, w + 2]$ $\phantom{-}1$
7 $[7, 7, w - 2]$ $\phantom{-}1$
9 $[9, 3, 3]$ $-2$
11 $[11, 11, -w]$ $\phantom{-}0$
19 $[19, 19, 2w - 5]$ $-2$
19 $[19, 19, -2w - 5]$ $-2$
37 $[37, 37, 2w - 9]$ $-6$
37 $[37, 37, -2w - 9]$ $-6$
43 $[43, 43, 2w - 1]$ $\phantom{-}8$
43 $[43, 43, -2w - 1]$ $\phantom{-}8$
53 $[53, 53, -w - 8]$ $-10$
53 $[53, 53, w - 8]$ $-10$
79 $[79, 79, 5w - 14]$ $-8$
79 $[79, 79, 8w - 25]$ $-8$
83 $[83, 83, -3w - 4]$ $\phantom{-}6$
83 $[83, 83, 3w - 4]$ $\phantom{-}6$
89 $[89, 89, -w - 10]$ $\phantom{-}10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 3]$ $-1$
$7$ $[7, 7, w + 2]$ $-1$
$7$ $[7, 7, w - 2]$ $-1$