# Properties

 Base field $$\Q(\sqrt{55})$$ Weight [2, 2] Level norm 6 Level $[6, 6, -w - 7]$ Label 2.2.220.1-6.1-d 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 $[6, 6, -w - 7]$ Label 2.2.220.1-6.1-d Dimension 4 Is CM no Is base change no Parent newspace dimension 32

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 5x^{2}$$ $$\mathstrut +\mathstrut x$$ $$\mathstrut +\mathstrut 4$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-1$
3 $[3, 3, w + 1]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, -2w + 15]$ $-e^{3} - e^{2} + 4e + 1$
11 $[11, 11, 3w - 22]$ $\phantom{-}e^{2} - 5$
13 $[13, 13, w + 4]$ $\phantom{-}e^{2} - e - 3$
13 $[13, 13, w + 9]$ $-e^{3} - e^{2} + 5e$
17 $[17, 17, w + 2]$ $-2e^{3} + e^{2} + 7e - 3$
17 $[17, 17, w + 15]$ $\phantom{-}e^{3} - e^{2} - 6e + 4$
19 $[19, 19, -w - 6]$ $-e^{2} - e$
19 $[19, 19, w - 6]$ $\phantom{-}4e^{3} + 2e^{2} - 13e - 3$
23 $[23, 23, w + 3]$ $\phantom{-}3e^{3} + 4e^{2} - 10e - 8$
23 $[23, 23, w + 20]$ $\phantom{-}e^{3} - 2e^{2} - 3e + 4$
47 $[47, 47, w + 14]$ $\phantom{-}2e^{3} + e^{2} - 7e + 1$
47 $[47, 47, w + 33]$ $-2e^{3} - 5e^{2} + 3e + 14$
49 $[49, 7, -7]$ $\phantom{-}2e^{3} + 5e^{2} - 8e - 11$
67 $[67, 67, w + 16]$ $\phantom{-}3e^{3} + 10e^{2} - 8e - 22$
67 $[67, 67, w + 51]$ $\phantom{-}3e^{3} + 2e^{2} - 10e - 1$
73 $[73, 73, w + 36]$ $-7e^{3} - 5e^{2} + 19e + 10$
73 $[73, 73, w + 37]$ $-e^{3} - 7e^{2} + 3e + 21$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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