# Properties

 Base field $$\Q(\sqrt{55})$$ Weight [2, 2] Level norm 2 Level $[2, 2, w + 1]$ Label 2.2.220.1-2.1-c Dimension 8 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## 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 $[2, 2, w + 1]$ Label 2.2.220.1-2.1-c Dimension 8 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8}$$ $$\mathstrut +\mathstrut 16x^{6}$$ $$\mathstrut +\mathstrut 138x^{4}$$ $$\mathstrut -\mathstrut 272x^{2}$$ $$\mathstrut +\mathstrut 1369$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-\frac{1}{504}e^{6} - \frac{5}{168}e^{4} - \frac{55}{168}e^{2} + \frac{101}{504}$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{4}{3367}e^{7} + \frac{219}{13468}e^{5} + \frac{478}{3367}e^{3} + \frac{3011}{13468}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{113}{40404}e^{7} + \frac{363}{6734}e^{5} + \frac{7307}{13468}e^{3} + \frac{15157}{20202}e$
5 $[5, 5, -2w + 15]$ $\phantom{-}2$
11 $[11, 11, 3w - 22]$ $-\frac{4}{3367}e^{7} - \frac{219}{13468}e^{5} - \frac{478}{3367}e^{3} + \frac{10457}{13468}e$
13 $[13, 13, w + 4]$ $-\frac{5}{546}e^{6} - \frac{57}{364}e^{4} - \frac{275}{182}e^{2} + \frac{905}{1092}$
13 $[13, 13, w + 9]$ $-\frac{1}{364}e^{6} - \frac{2}{91}e^{4} - \frac{165}{364}e^{2} + \frac{34}{91}$
17 $[17, 17, w + 2]$ $\phantom{-}\frac{9}{728}e^{6} + \frac{163}{728}e^{4} + \frac{1485}{728}e^{2} - \frac{769}{728}$
17 $[17, 17, w + 15]$ $-\frac{1}{2184}e^{6} - \frac{33}{728}e^{4} - \frac{55}{728}e^{2} - \frac{319}{2184}$
19 $[19, 19, -w - 6]$ $-\frac{29}{3848}e^{7} - \frac{427}{3848}e^{5} - \frac{3225}{3848}e^{3} + \frac{17841}{3848}e$
19 $[19, 19, w - 6]$ $-\frac{3}{3848}e^{7} - \frac{11}{3848}e^{5} - \frac{599}{3848}e^{3} + \frac{3073}{3848}e$
23 $[23, 23, w + 3]$ $-\frac{5}{1554}e^{7} - \frac{39}{518}e^{5} - \frac{415}{518}e^{3} - \frac{1637}{1554}e$
23 $[23, 23, w + 20]$ $\phantom{-}\frac{5}{1554}e^{7} + \frac{39}{518}e^{5} + \frac{415}{518}e^{3} + \frac{1637}{1554}e$
47 $[47, 47, w + 14]$ $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$
49 $[49, 7, -7]$ $\phantom{-}3$
67 $[67, 67, w + 16]$ $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$
67 $[67, 67, w + 51]$ $\phantom{-}\frac{23}{5772}e^{7} + \frac{135}{1924}e^{5} + \frac{1317}{1924}e^{3} + \frac{5621}{5772}e$
73 $[73, 73, w + 36]$ $-\frac{1}{182}e^{6} - \frac{4}{91}e^{4} - \frac{165}{182}e^{2} + \frac{68}{91}$
73 $[73, 73, w + 37]$ $-\frac{5}{273}e^{6} - \frac{57}{182}e^{4} - \frac{275}{91}e^{2} + \frac{905}{546}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\frac{1}{504}e^{6} + \frac{5}{168}e^{4} + \frac{55}{168}e^{2} - \frac{101}{504}$