# Properties

 Base field 4.4.4205.1 Weight [2, 2, 2, 2] Level norm 53 Level $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ Label 4.4.4205.1-53.1-a Dimension 4 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 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ Label 4.4.4205.1-53.1-a Dimension 4 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:
$$x^{4}$$ $$\mathstrut -\mathstrut 2x^{3}$$ $$\mathstrut -\mathstrut 10x^{2}$$ $$\mathstrut +\mathstrut 4x$$ $$\mathstrut +\mathstrut 12$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + 3e - 1$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $-\frac{1}{2}e^{2} + e + 2$
13 $[13, 13, -w^{2} + w + 3]$ $-\frac{1}{2}e^{2} + 2e + 2$
13 $[13, 13, -w^{2} + w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 4e + 2$
16 $[16, 2, 2]$ $-e + 5$
23 $[23, 23, -w^{2} + 3w + 1]$ $\phantom{-}e^{2} - e - 6$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - 3e + 6$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{1}{2}e^{3} + 2e^{2} + 2e - 4$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $-e^{3} + \frac{5}{2}e^{2} + 5e - 7$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $-1$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}\frac{3}{2}e^{2} - 3e - 9$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $-e^{3} + 2e^{2} + 6e - 4$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $\phantom{-}\frac{3}{2}e^{3} - 5e^{2} - 9e + 14$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 8e + 4$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 5e - 3$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $-\frac{1}{2}e^{3} + 2e^{2} + 3e - 6$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $\phantom{-}e^{3} - 5e^{2} - e + 20$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $\phantom{-}\frac{1}{2}e^{3} - 3e^{2} - 2e + 8$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $-2e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $1$