# Properties

 Label 4.4.5744.1-13.1-b Base field 4.4.5744.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, -w^{3} + w^{2} + 4w]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.5744.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13, 13, -w^{3} + w^{2} + 4w]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 21x^{2} + 96$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-\frac{1}{4}e^{3} + \frac{13}{4}e$
7 $[7, 7, -w^{2} + w + 2]$ $-\frac{1}{4}e^{3} + \frac{9}{4}e$
13 $[13, 13, -w^{3} + w^{2} + 4w]$ $-1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$
17 $[17, 17, -w^{2} + 2]$ $-2e$
19 $[19, 19, -w^{3} + 5w]$ $-\frac{1}{4}e^{3} + \frac{13}{4}e$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}e^{2} - 14$
37 $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ $\phantom{-}2e$
43 $[43, 43, -w - 3]$ $\phantom{-}2e^{2} - 20$
53 $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{21}{4}e$
53 $[53, 53, w^{3} - 6w - 2]$ $\phantom{-}e^{2} - 6$
59 $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ $\phantom{-}e^{2}$
61 $[61, 61, 2w^{3} - w^{2} - 10w]$ $-e^{2} + 10$
61 $[61, 61, 2w^{3} - w^{2} - 8w]$ $\phantom{-}\frac{3}{4}e^{3} - \frac{31}{4}e$
71 $[71, 71, 2w^{3} - 9w - 2]$ $-\frac{1}{4}e^{3} + \frac{21}{4}e$
73 $[73, 73, -w^{3} - w^{2} + 6w + 3]$ $\phantom{-}e^{3} - 13e$
81 $[81, 3, -3]$ $-e^{2} + 16$
83 $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{1}{2}e^{3} + \frac{11}{2}e$
101 $[101, 101, 2w^{3} - 8w - 3]$ $-\frac{3}{4}e^{3} + \frac{39}{4}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{3} + w^{2} + 4w]$ $1$