# Properties

 Base field $$\Q(\sqrt{114})$$ Weight [2, 2] Level norm 2 Level $[2, 2, -3w - 32]$ Label 2.2.456.1-2.1-m Dimension 4 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 $[2, 2, -3w - 32]$ Label 2.2.456.1-2.1-m Dimension 4 Is CM no Is base change no Parent newspace dimension 28

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 14x^{2}$$ $$\mathstrut +\mathstrut 36$$
Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $\phantom{-}1$
3 $[3, 3, w]$ $-\frac{1}{6}e^{3} + \frac{4}{3}e$
5 $[5, 5, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{7}{3}e$
7 $[7, 7, -w + 11]$ $\phantom{-}e^{2} - 8$
7 $[7, 7, w + 11]$ $-e^{2} + 6$
11 $[11, 11, w + 2]$ $-\frac{1}{3}e^{3} + \frac{8}{3}e$
11 $[11, 11, w + 9]$ $-\frac{1}{3}e^{3} + \frac{8}{3}e$
13 $[13, 13, w + 6]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{5}{3}e$
13 $[13, 13, w + 7]$ $\phantom{-}\frac{1}{2}e^{3} - 5e$
19 $[19, 19, w]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{4}{3}e$
37 $[37, 37, w + 15]$ $-\frac{1}{2}e^{3} + 5e$
37 $[37, 37, w + 22]$ $-\frac{1}{3}e^{3} + \frac{5}{3}e$
41 $[41, 41, 37w + 395]$ $\phantom{-}e^{2} - 12$
41 $[41, 41, 5w + 53]$ $-e^{2} + 2$
67 $[67, 67, w + 28]$ $\phantom{-}0$
67 $[67, 67, w + 39]$ $\phantom{-}0$
71 $[71, 71, 40w + 427]$ $\phantom{-}e^{2} - 18$
71 $[71, 71, 8w + 85]$ $-e^{2} - 4$
73 $[73, 73, -2w + 23]$ $\phantom{-}2e^{2} - 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $-1$