# Properties

 Label 4.4.8789.1-13.1-c Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ Dimension $5$ 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: $5$ 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:

 $$x^{5} + 4x^{4} - 4x^{3} - 21x^{2} - x + 20$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}2e^{4} + 5e^{3} - 15e^{2} - 17e + 23$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-e^{2} - 2e + 4$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-1$
16 $[16, 2, 2]$ $-2e^{4} - 5e^{3} + 14e^{2} + 16e - 19$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-3e^{4} - 7e^{3} + 24e^{2} + 25e - 34$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-e^{2} - e + 4$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 10e + 9$
19 $[19, 19, w^{2} - w - 2]$ $-2e^{4} - 5e^{3} + 15e^{2} + 20e - 20$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-e^{4} - 2e^{3} + 9e^{2} + 6e - 16$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}2e^{4} + 4e^{3} - 18e^{2} - 12e + 31$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-2e^{4} - 5e^{3} + 14e^{2} + 17e - 17$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}e^{4} + 2e^{3} - 9e^{2} - 7e + 12$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}3e^{4} + 7e^{3} - 24e^{2} - 22e + 40$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}3e^{4} + 7e^{3} - 25e^{2} - 25e + 44$
61 $[61, 61, -w - 3]$ $-3e^{4} - 6e^{3} + 29e^{2} + 21e - 54$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}3e^{4} + 8e^{3} - 20e^{2} - 25e + 32$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}e^{4} + 3e^{3} - 8e^{2} - 14e + 14$
81 $[81, 3, -3]$ $\phantom{-}5e^{4} + 11e^{3} - 40e^{2} - 35e + 65$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-4e^{4} - 8e^{3} + 35e^{2} + 27e - 54$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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