# Properties

 Label 2.2.12.1-81.1-a Base field $$\Q(\sqrt{3})$$ Weight $[2, 2]$ Level norm $81$ Level $[81, 9, 9]$ Dimension $1$ CM yes Base change yes

# Related objects

## Base field $$\Q(\sqrt{3})$$

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

## Form

 Weight: $[2, 2]$ Level: $[81, 9, 9]$ Dimension: $1$ CM: yes Base change: yes Newspace dimension: $5$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}0$
11 $[11, 11, -2w + 1]$ $\phantom{-}0$
11 $[11, 11, 2w + 1]$ $\phantom{-}0$
13 $[13, 13, w + 4]$ $\phantom{-}5$
13 $[13, 13, -w + 4]$ $\phantom{-}5$
23 $[23, 23, -3w + 2]$ $\phantom{-}0$
23 $[23, 23, 3w + 2]$ $\phantom{-}0$
25 $[25, 5, 5]$ $-10$
37 $[37, 37, 2w - 7]$ $\phantom{-}11$
37 $[37, 37, -2w - 7]$ $\phantom{-}11$
47 $[47, 47, -4w - 1]$ $\phantom{-}0$
47 $[47, 47, 4w - 1]$ $\phantom{-}0$
49 $[49, 7, -7]$ $-13$
59 $[59, 59, 5w - 4]$ $\phantom{-}0$
59 $[59, 59, -5w - 4]$ $\phantom{-}0$
61 $[61, 61, -w - 8]$ $-1$
61 $[61, 61, w - 8]$ $-1$
71 $[71, 71, 5w - 2]$ $\phantom{-}0$
71 $[71, 71, -5w - 2]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$