# Properties

 Base field 4.4.4205.1 Weight [2, 2, 2, 2] Level norm 13 Level $[13,13,w^{2} - w - 2]$ Label 4.4.4205.1-13.2-b Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.4205.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 5x^{2} - x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[13,13,w^{2} - w - 2]$ Label 4.4.4205.1-13.2-b Dimension 3 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:
$$x^{3}$$ $$\mathstrut -\mathstrut 3x^{2}$$ $$\mathstrut -\mathstrut 5x$$ $$\mathstrut +\mathstrut 13$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $-e^{2} + 2e + 4$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $\phantom{-}e^{2} - 7$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}e^{2} - 2e - 3$
13 $[13, 13, -w^{2} + w + 2]$ $-1$
16 $[16, 2, 2]$ $-e^{2} + e + 5$
23 $[23, 23, -w^{2} + 3w + 1]$ $-e^{2} + e + 5$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $-e^{2} - 2e + 9$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-e^{2} + 2e + 1$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $-e$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $-e^{2} + 13$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}3e^{2} - 4e - 9$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $-e^{2} + e + 7$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $\phantom{-}e^{2} + 2e - 8$
81 $[81, 3, -3]$ $-2e + 3$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $\phantom{-}7$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $\phantom{-}e^{2} - 3e - 11$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $-e^{2} + 4e + 4$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $\phantom{-}e^{2} - 4e + 1$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}2e^{2} - 6e - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13,13,w^{2} - w - 2]$ $1$