# Properties

 Label 5.5.157457.1-21.1-j Base field 5.5.157457.1 Weight $[2, 2, 2, 2, 2]$ Level norm $21$ Level $[21, 21, w^{4} - 3w^{3} - w^{2} + 6w - 3]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 5.5.157457.1

Generator $$w$$, with minimal polynomial $$x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2]$ Level: $[21, 21, w^{4} - 3w^{3} - w^{2} + 6w - 3]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $15$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 3x - 6$$
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}1$
5 $[5, 5, w^{2} - w - 2]$ $\phantom{-}e$
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $\phantom{-}1$
13 $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ $-3$
29 $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ $-e - 3$
29 $[29, 29, -w^{2} + 2w + 3]$ $-e - 5$
31 $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-6$
31 $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}1$
32 $[32, 2, 2]$ $-2e - 7$
43 $[43, 43, -w^{2} - w + 4]$ $\phantom{-}e - 5$
53 $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ $-e - 8$
53 $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $-e + 3$
73 $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ $\phantom{-}e - 1$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e + 4$
81 $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ $\phantom{-}4e + 10$
83 $[83, 83, w^{3} - w^{2} - 5w]$ $\phantom{-}4e + 9$
89 $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ $-e + 2$
97 $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $\phantom{-}3e - 6$
101 $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ $-6e - 7$
103 $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ $-e + 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w - 1]$ $-1$
$7$ $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $-1$