# Properties

 Label 4.4.16448.1-10.2-b Base field 4.4.16448.1 Weight $[2, 2, 2, 2]$ Level norm $10$ Level $[10, 10, -w^{3} + 3w^{2} + 3w]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16448.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[10, 10, -w^{3} + 3w^{2} + 3w]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} - x^{2} - 4x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-e^{2} + 2e + 5$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $-2e^{2} + 3e + 6$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $\phantom{-}e^{2} - 3e$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-3e^{2} + 5e + 9$
25 $[25, 5, -w^{2} + 3w + 1]$ $\phantom{-}2e^{2} - 2e - 3$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $-e^{2} + 4$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}5e^{2} - 7e - 13$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $\phantom{-}e^{2} - 4e + 1$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $-e^{2} + 2e + 6$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $\phantom{-}5e^{2} - 7e - 16$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $\phantom{-}e^{2} - 3e - 6$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-3e^{2} - e + 8$
81 $[81, 3, -3]$ $-9e^{2} + 13e + 18$
83 $[83, 83, -w - 3]$ $\phantom{-}e^{2} + 3e - 1$
83 $[83, 83, w^{2} - 3w - 7]$ $\phantom{-}5e^{2} - 3e - 16$
89 $[89, 89, w^{2} - 2w - 7]$ $\phantom{-}e^{2} + e - 14$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-2e^{2} - 3e + 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$5$ $[5, 5, w - 1]$ $-1$