# Properties

 Base field $$\Q(\sqrt{55})$$ Weight [2, 2] Level norm 4 Level $[4, 2, 2]$ Label 2.2.220.1-4.1-b Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{55})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 55$$; narrow class number $$4$$ and class number $$2$$.

## Form

 Weight [2, 2] Level $[4, 2, 2]$ Label 2.2.220.1-4.1-b Dimension 4 Is CM no Is base change no Parent newspace dimension 16

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 16x^{2}$$ $$\mathstrut +\mathstrut 3136$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}0$
3 $[3, 3, w + 2]$ $\phantom{-}0$
5 $[5, 5, -2w + 15]$ $\phantom{-}2$
11 $[11, 11, 3w - 22]$ $-\frac{1}{112}e^{3} + \frac{9}{14}e$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{1}{112}e^{3} + \frac{5}{14}e$
13 $[13, 13, w + 9]$ $-\frac{1}{112}e^{3} - \frac{5}{14}e$
17 $[17, 17, w + 2]$ $-\frac{1}{112}e^{3} - \frac{5}{14}e$
17 $[17, 17, w + 15]$ $\phantom{-}\frac{1}{112}e^{3} + \frac{5}{14}e$
19 $[19, 19, -w - 6]$ $\phantom{-}\frac{1}{112}e^{3} - \frac{9}{14}e$
19 $[19, 19, w - 6]$ $\phantom{-}\frac{1}{112}e^{3} - \frac{9}{14}e$
23 $[23, 23, w + 3]$ $\phantom{-}\frac{1}{8}e^{2} - 1$
23 $[23, 23, w + 20]$ $-\frac{1}{8}e^{2} + 1$
47 $[47, 47, w + 14]$ $\phantom{-}\frac{1}{8}e^{2} - 1$
47 $[47, 47, w + 33]$ $-\frac{1}{8}e^{2} + 1$
49 $[49, 7, -7]$ $\phantom{-}6$
67 $[67, 67, w + 16]$ $\phantom{-}\frac{1}{4}e^{2} - 2$
67 $[67, 67, w + 51]$ $-\frac{1}{4}e^{2} + 2$
73 $[73, 73, w + 36]$ $-\frac{1}{112}e^{3} - \frac{5}{14}e$
73 $[73, 73, w + 37]$ $\phantom{-}\frac{1}{112}e^{3} + \frac{5}{14}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $1$