# Properties

 Base field $$\Q(\sqrt{114})$$ Weight [2, 2] Level norm 3 Level $[3, 3, w]$ Label 2.2.456.1-3.1-c Dimension 6 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{114})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 114$$; narrow class number $$4$$ and class number $$2$$.

## Form

 Weight [2, 2] Level $[3, 3, w]$ Label 2.2.456.1-3.1-c Dimension 6 Is CM no Is base change no Parent newspace dimension 72

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 23x^{4}$$ $$\mathstrut +\mathstrut 152x^{2}$$ $$\mathstrut -\mathstrut 236$$
Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $\phantom{-}0$
3 $[3, 3, w]$ $-1$
5 $[5, 5, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $-e$
7 $[7, 7, -w + 11]$ $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{13}{2}$
7 $[7, 7, w + 11]$ $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{13}{2}$
11 $[11, 11, w + 2]$ $-\frac{1}{8}e^{5} + \frac{17}{8}e^{3} - \frac{29}{4}e$
11 $[11, 11, w + 9]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{17}{8}e^{3} + \frac{29}{4}e$
13 $[13, 13, w + 6]$ $-\frac{3}{8}e^{4} + \frac{43}{8}e^{2} - \frac{47}{4}$
13 $[13, 13, w + 7]$ $-\frac{3}{8}e^{4} + \frac{43}{8}e^{2} - \frac{47}{4}$
19 $[19, 19, w]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{9}{4}e^{2} - \frac{3}{2}$
37 $[37, 37, w + 15]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{25}{8}e^{2} + \frac{53}{4}$
37 $[37, 37, w + 22]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{25}{8}e^{2} + \frac{53}{4}$
41 $[41, 41, 37w + 395]$ $-\frac{1}{8}e^{5} + \frac{9}{8}e^{3} + \frac{3}{4}e$
41 $[41, 41, 5w + 53]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{9}{8}e^{3} - \frac{3}{4}e$
67 $[67, 67, w + 28]$ $-\frac{3}{4}e^{4} + \frac{43}{4}e^{2} - \frac{47}{2}$
67 $[67, 67, w + 39]$ $-\frac{3}{4}e^{4} + \frac{43}{4}e^{2} - \frac{47}{2}$
71 $[71, 71, 40w + 427]$ $-\frac{1}{4}e^{5} + \frac{17}{4}e^{3} - \frac{33}{2}e$
71 $[71, 71, 8w + 85]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{17}{4}e^{3} + \frac{33}{2}e$
73 $[73, 73, -2w + 23]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $1$