# Properties

 Label 4.4.16448.1-20.2-e Base field 4.4.16448.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, -w^{2} + 2w + 4]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16448.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 6x^{2} + 2$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, -w^{2} + 2w + 4]$ Dimension: $6$ 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:

 $$x^{6} - 24x^{4} + 128x^{2} - 64$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{1}{4}e^{3} + 3e$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{1}{8}e^{4} + \frac{5}{2}e^{2} - 4$
25 $[25, 5, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{16}e^{5} - \frac{5}{4}e^{3} + 3e$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 15e$
31 $[31, 31, -w^{2} + 2w + 1]$ $-\frac{1}{4}e^{3} + 3e$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $-\frac{1}{8}e^{4} + \frac{7}{2}e^{2} - 12$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $-\frac{1}{8}e^{5} + \frac{13}{4}e^{3} - 17e$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $-\frac{1}{8}e^{4} + \frac{3}{2}e^{2} + 4$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 16$
81 $[81, 3, -3]$ $-\frac{1}{4}e^{4} + 5e^{2} - 14$
83 $[83, 83, -w - 3]$ $\phantom{-}\frac{3}{8}e^{4} - \frac{13}{2}e^{2} + 20$
83 $[83, 83, w^{2} - 3w - 7]$ $-e^{2} + 8$
89 $[89, 89, w^{2} - 2w - 7]$ $-\frac{1}{4}e^{4} + 3e^{2} + 2$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$5$ $[5, 5, w - 1]$ $-1$