# Properties

 Label 2.2.33.1-192.1-f Base field $$\Q(\sqrt{33})$$ Weight $[2, 2]$ Level norm $192$ Level $[192, 24, 16w - 56]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{33})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 8$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[192, 24, 16w - 56]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, -w + 3]$ $\phantom{-}0$
3 $[3, 3, 2w - 7]$ $-1$
11 $[11, 11, 4w - 13]$ $\phantom{-}4$
17 $[17, 17, -2w + 5]$ $\phantom{-}2$
17 $[17, 17, 2w + 3]$ $\phantom{-}2$
25 $[25, 5, 5]$ $-6$
29 $[29, 29, -2w + 3]$ $\phantom{-}6$
29 $[29, 29, 2w + 1]$ $\phantom{-}6$
31 $[31, 31, -2w + 9]$ $\phantom{-}8$
31 $[31, 31, 2w + 7]$ $\phantom{-}8$
37 $[37, 37, -4w - 11]$ $\phantom{-}6$
37 $[37, 37, 4w - 15]$ $\phantom{-}6$
41 $[41, 41, -10w + 33]$ $-6$
41 $[41, 41, 6w - 19]$ $-6$
49 $[49, 7, -7]$ $-14$
67 $[67, 67, 2w - 11]$ $-4$
67 $[67, 67, -2w - 9]$ $-4$
83 $[83, 83, 4w + 5]$ $-4$
83 $[83, 83, 4w - 9]$ $-4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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