# Properties

 Label 4.4.8789.1-13.1-b Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ 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:

 $$x^{4} - 12x^{2} - x + 3$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{11}{3}e + 1$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - \frac{22}{3}e$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $\phantom{-}1$
16 $[16, 2, 2]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{14}{3}e - 5$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-e^{3} + 10e - 1$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{19}{3}e - 4$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}e^{3} - 13e$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{14}{3}e - 2$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - \frac{25}{3}e - 1$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}\frac{4}{3}e^{3} - \frac{2}{3}e^{2} - \frac{44}{3}e - 1$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e^{3} - 11e - 3$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-\frac{4}{3}e^{3} - \frac{1}{3}e^{2} + \frac{44}{3}e - 1$
47 $[47, 47, w^{3} - 7w - 4]$ $-e^{3} + 13e + 3$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-e^{3} + e^{2} + 14e - 5$
61 $[61, 61, -w - 3]$ $\phantom{-}\frac{4}{3}e^{3} + \frac{1}{3}e^{2} - \frac{44}{3}e - 3$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-2e - 5$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $-\frac{5}{3}e^{3} - \frac{2}{3}e^{2} + \frac{55}{3}e - 1$
81 $[81, 3, -3]$ $-e^{3} + 14e - 2$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{31}{3}e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-1$