# Properties

 Label 4.4.13768.1-12.2-h Base field 4.4.13768.1 Weight $[2, 2, 2, 2]$ Level norm $12$ Level $[12, 6, -w^{3} + 2w^{2} + 4w - 5]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13768.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[12, 6, -w^{3} + 2w^{2} + 4w - 5]$ Dimension: $4$ 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:

 $$x^{4} + x^{3} - 7x^{2} - 7x + 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}1$
4 $[4, 2, -w^{2} - w + 1]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}e^{3} + e^{2} - 6e - 4$
17 $[17, 17, -w + 3]$ $-2e - 2$
27 $[27, 3, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}e^{3} - e^{2} - 6e + 2$
31 $[31, 31, -w^{2} - 2w + 1]$ $\phantom{-}e^{2} - e$
41 $[41, 41, -w^{2} + 5]$ $-2e^{3} + 12e + 8$
43 $[43, 43, w^{3} - w^{2} - 5w - 1]$ $-e^{3} - 2e^{2} + 9e + 10$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 4$
59 $[59, 59, -w - 3]$ $\phantom{-}e^{3} - 7e + 2$
59 $[59, 59, -2w^{3} + 2w^{2} + 9w - 5]$ $\phantom{-}e^{3} - 5e - 4$
59 $[59, 59, -w^{3} - 3w^{2} - w + 3]$ $\phantom{-}2e^{3} + 2e^{2} - 10e - 8$
59 $[59, 59, w^{3} - 7w + 1]$ $\phantom{-}3e^{3} - 21e - 10$
61 $[61, 61, -w^{3} + w^{2} + 2w + 5]$ $\phantom{-}e^{3} - 7e + 4$
61 $[61, 61, -w^{3} - w^{2} + 4w + 3]$ $-2e^{3} + 12e + 2$
67 $[67, 67, 4w^{3} - 4w^{2} - 18w + 7]$ $-2e - 4$
73 $[73, 73, -2w^{3} + 6w - 3]$ $-2e^{3} - 3e^{2} + 13e + 12$
73 $[73, 73, -2w + 3]$ $-2e^{3} + 2e^{2} + 12e - 4$
97 $[97, 97, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}2e^{2} - 2e - 18$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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