# Properties

 Label 4.4.13676.1-20.1-g Base field 4.4.13676.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, -w^{2} - w + 5]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13676.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} + 7x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, -w^{2} - w + 5]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $23$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - x^{3} - 7x^{2} + 5x + 6$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}1$
5 $[5, 5, w^{3} - 5w + 1]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + 6w - 2]$ $\phantom{-}e^{2} + e - 6$
13 $[13, 13, -w^{2} + 4]$ $-2e + 2$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $-e^{2} + e + 6$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $-2e^{3} + 10e + 2$
37 $[37, 37, -w^{3} + 6w - 4]$ $\phantom{-}e^{3} - 2e^{2} - 3e + 8$
41 $[41, 41, -w^{3} + 5w - 5]$ $\phantom{-}e^{2} - e$
43 $[43, 43, w^{3} - 4w + 4]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 8$
43 $[43, 43, -2w^{3} + 11w - 2]$ $-e^{3} - e^{2} + 6e + 2$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $\phantom{-}e^{3} - 7e + 6$
47 $[47, 47, 2w - 1]$ $-2e^{3} + 12e$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}2e^{2} - 10$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}2e^{2} - 2e - 6$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $-e^{3} - 2e^{2} + 5e + 12$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}e^{3} - 4e^{2} - 5e + 14$
81 $[81, 3, -3]$ $\phantom{-}2e^{3} - 2e^{2} - 10e + 4$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $\phantom{-}e^{3} - 2e^{2} - 3e$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $-2e^{3} + 3e^{2} + 11e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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