# Properties

 Base field 4.4.9909.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11, 11, -w^{2} + w + 2]$ Label 4.4.9909.1-11.1-b Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.9909.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - 3x + 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[11, 11, -w^{2} + w + 2]$ Label 4.4.9909.1-11.1-b Dimension 2 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}2$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e + 1$
11 $[11, 11, -w^{2} + w + 2]$ $-1$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $-e$
16 $[16, 2, 2]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + 5w + 2]$ $\phantom{-}4e + 2$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}4e + 2$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}7e + 5$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}0$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}2e + 6$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $-6e$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}4e + 6$
53 $[53, 53, w^{3} - 4w - 4]$ $-6e - 2$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $\phantom{-}2e + 8$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-5e + 1$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $-10e - 2$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $-7e - 9$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $-8e - 12$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $-3e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{2} + w + 2]$ $1$