# Properties

 Label 4.4.17609.1-20.1-d Base field 4.4.17609.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 20, w^{3} + w^{2} - 5w - 1]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17609.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 10x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 20, w^{3} + w^{2} - 5w - 1]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} + x^{3} - 24x^{2} - 44x - 16$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + 6w - 2]$ $\phantom{-}e$
8 $[8, 2, w^{3} - 7w + 3]$ $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{11}{2}e + 3$
11 $[11, 11, -w^{3} + 6w - 4]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 6e + 7$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 7e - 7$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}4$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 6e + 3$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 5e - 11$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 10e - 2$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 12e - 4$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $-\frac{3}{4}e^{3} + \frac{1}{4}e^{2} + 18e + 17$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 13e - 18$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-\frac{3}{4}e^{3} + \frac{1}{4}e^{2} + 17e + 15$
59 $[59, 59, w^{2} + w - 1]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 8e + 15$
59 $[59, 59, w^{2} + 2w - 6]$ $\phantom{-}e^{3} - 24e - 20$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 12e + 14$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}4$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $\phantom{-}e^{3} - 24e - 16$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 10e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $-1$
$5$ $[5, 5, w^{3} + w^{2} - 4w + 1]$ $-1$