# Properties

 Label 2.2.12.1-37.2-a Base field $$\Q(\sqrt{3})$$ Weight $[2, 2]$ Level norm $37$ Level $[37,37,-2w - 7]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## 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: $[37,37,-2w - 7]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 5x^{2} + 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-e^{3} + 4e$
11 $[11, 11, -2w + 1]$ $\phantom{-}e^{3} - 5e$
11 $[11, 11, 2w + 1]$ $\phantom{-}e^{3} - 5e$
13 $[13, 13, w + 4]$ $\phantom{-}2e^{2} - 4$
13 $[13, 13, -w + 4]$ $-e^{2} + 4$
23 $[23, 23, -3w + 2]$ $\phantom{-}2e^{3} - 10e$
23 $[23, 23, 3w + 2]$ $-2e^{3} + 7e$
25 $[25, 5, 5]$ $-2e^{2} + 6$
37 $[37, 37, 2w - 7]$ $-3e^{2} + 8$
37 $[37, 37, -2w - 7]$ $-1$
47 $[47, 47, -4w - 1]$ $\phantom{-}3e^{3} - 11e$
47 $[47, 47, 4w - 1]$ $-2e^{3} + 15e$
49 $[49, 7, -7]$ $\phantom{-}5e^{2} - 14$
59 $[59, 59, 5w - 4]$ $\phantom{-}3e^{3} - 7e$
59 $[59, 59, -5w - 4]$ $-7e^{3} + 26e$
61 $[61, 61, -w - 8]$ $-2e^{2} + 4$
61 $[61, 61, w - 8]$ $\phantom{-}e^{2} - 4$
71 $[71, 71, 5w - 2]$ $\phantom{-}2e^{3} - 13e$
71 $[71, 71, -5w - 2]$ $\phantom{-}5e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37,37,-2w - 7]$ $1$