# Properties

 Base field 4.4.4205.1 Weight [2, 2, 2, 2] Level norm 35 Level $[35,35,2w^{3} - 4w^{2} - 7w + 4]$ Label 4.4.4205.1-35.2-c 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 $[35,35,2w^{3} - 4w^{2} - 7w + 4]$ Label 4.4.4205.1-35.2-c Dimension 3 Is CM no Is base change no Parent newspace dimension 5

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut +\mathstrut 2x^{2}$$ $$\mathstrut -\mathstrut 16x$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}1$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}2$
13 $[13, 13, -w^{2} + w + 2]$ $-\frac{1}{2}e^{2} - e + 6$
16 $[16, 2, 2]$ $\phantom{-}e + 3$
23 $[23, 23, -w^{2} + 3w + 1]$ $\phantom{-}0$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $-\frac{1}{2}e^{2} - e + 4$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{2}e^{2} - 6$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - 6$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $-6$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $-e + 2$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $-2e$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $-e^{2} + 12$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{2} - e + 2$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $-e^{2} - 2e + 8$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $\phantom{-}\frac{3}{2}e^{2} + 3e - 12$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $\phantom{-}e^{2} - 2e - 16$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $-\frac{1}{2}e^{2} + 2e + 12$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5,5,w - 1]$ $-1$
7 $[7,7,-w^{3} + 2w^{2} + 3w - 3]$ $-1$