# Properties

 Base field 4.4.9909.1 Weight [2, 2, 2, 2] Level norm 17 Level $[17, 17, -w^{3} + 5w + 2]$ Label 4.4.9909.1-17.1-c Dimension 3 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 $[17, 17, -w^{3} + 5w + 2]$ Label 4.4.9909.1-17.1-c Dimension 3 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:
$$x^{3}$$ $$\mathstrut -\mathstrut 3x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}e^{2} - 1$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{2} - 2e - 3$
11 $[11, 11, -w^{2} + w + 2]$ $-2e^{2} - e + 3$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $-2e^{2} + e + 3$
16 $[16, 2, 2]$ $\phantom{-}3e^{2} - 7$
17 $[17, 17, -w^{3} + 5w + 2]$ $\phantom{-}1$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}e^{2} - e - 9$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $-3e + 2$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $-5e^{2} + 3e + 8$
41 $[41, 41, w^{2} - 5]$ $-4e^{2} + e + 9$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $-5e^{2} + 2e + 9$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}3e^{2} - 5e - 7$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}e^{2} + e - 8$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $\phantom{-}3e$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-2e^{2} + 4e + 6$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $-8e^{2} + 7e + 13$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $-11e^{2} + 7e + 21$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $-5e^{2} + 10e + 15$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $\phantom{-}5e^{2} - e - 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{3} + 5w + 2]$ $-1$