# Properties

 Label 2.2.12.1-61.2-a Base field $$\Q(\sqrt{3})$$ Weight $[2, 2]$ Level norm $61$ Level $[61,61,w - 8]$ Dimension $6$ 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: $[61,61,w - 8]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 10x^{4} + 23x^{2} - 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$
11 $[11, 11, -2w + 1]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 13e$
11 $[11, 11, 2w + 1]$ $\phantom{-}e^{3} - 5e$
13 $[13, 13, w + 4]$ $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 1$
13 $[13, 13, -w + 4]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 5$
23 $[23, 23, -3w + 2]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$
23 $[23, 23, 3w + 2]$ $\phantom{-}e^{5} - 11e^{3} + 26e$
25 $[25, 5, 5]$ $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 5$
37 $[37, 37, 2w - 7]$ $-e^{4} + 7e^{2} - 6$
37 $[37, 37, -2w - 7]$ $-\frac{1}{2}e^{4} + \frac{3}{2}e^{2} + 3$
47 $[47, 47, -4w - 1]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} - 6e$
47 $[47, 47, 4w - 1]$ $-\frac{3}{2}e^{5} + \frac{33}{2}e^{3} - 42e$
49 $[49, 7, -7]$ $-2e^{2} + 6$
59 $[59, 59, 5w - 4]$ $\phantom{-}e^{5} - 8e^{3} + 11e$
59 $[59, 59, -5w - 4]$ $\phantom{-}e^{5} - 9e^{3} + 20e$
61 $[61, 61, -w - 8]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{2} - 5$
61 $[61, 61, w - 8]$ $-1$
71 $[71, 71, 5w - 2]$ $\phantom{-}e^{5} - 7e^{3} + 6e$
71 $[71, 71, -5w - 2]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{31}{2}e^{3} + 42e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$61$ $[61,61,w - 8]$ $1$