# Properties

 Base field $$\Q(\sqrt{55})$$ Weight [2, 2] Level norm 3 Level $[3, 3, w + 1]$ Label 2.2.220.1-3.1-c Dimension 16 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 $[3, 3, w + 1]$ Label 2.2.220.1-3.1-c Dimension 16 Is CM no Is base change no Parent newspace dimension 24

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{16}$$ $$\mathstrut +\mathstrut 60x^{14}$$ $$\mathstrut +\mathstrut 1346x^{12}$$ $$\mathstrut +\mathstrut 14040x^{10}$$ $$\mathstrut +\mathstrut 67921x^{8}$$ $$\mathstrut +\mathstrut 129884x^{6}$$ $$\mathstrut +\mathstrut 74064x^{4}$$ $$\mathstrut +\mathstrut 13504x^{2}$$ $$\mathstrut +\mathstrut 256$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $...$
3 $[3, 3, w + 1]$ $-\frac{11523}{1313824}e^{15} - \frac{686685}{1313824}e^{13} - \frac{951877}{82114}e^{11} - \frac{9723097}{82114}e^{9} - \frac{719100509}{1313824}e^{7} - \frac{1202061251}{1313824}e^{5} - \frac{11145560}{41057}e^{3} + \frac{59629}{41057}e$
3 $[3, 3, w + 2]$ $...$
5 $[5, 5, -2w + 15]$ $...$
11 $[11, 11, 3w - 22]$ $...$
13 $[13, 13, w + 4]$ $...$
13 $[13, 13, w + 9]$ $...$
17 $[17, 17, w + 2]$ $...$
17 $[17, 17, w + 15]$ $...$
19 $[19, 19, -w - 6]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 3]$ $...$
23 $[23, 23, w + 20]$ $...$
47 $[47, 47, w + 14]$ $...$
47 $[47, 47, w + 33]$ $...$
49 $[49, 7, -7]$ $...$
67 $[67, 67, w + 16]$ $...$
67 $[67, 67, w + 51]$ $...$
73 $[73, 73, w + 36]$ $...$
73 $[73, 73, w + 37]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\frac{11523}{1313824}e^{15} + \frac{686685}{1313824}e^{13} + \frac{951877}{82114}e^{11} + \frac{9723097}{82114}e^{9} + \frac{719100509}{1313824}e^{7} + \frac{1202061251}{1313824}e^{5} + \frac{11145560}{41057}e^{3} - \frac{59629}{41057}e$