# Properties

 Label 4.4.16609.1-12.1-a Base field 4.4.16609.1 Weight $[2, 2, 2, 2]$ Level norm $12$ Level $[12, 12, -w^{3} + w^{2} + 3w - 3]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16609.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} - x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[12, 12, -w^{3} + w^{2} + 3w - 3]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + x^{2} - 9x + 3$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}0$
3 $[3, 3, -w^{2} + w + 3]$ $-1$
5 $[5, 5, w^{2} - 4]$ $\phantom{-}e$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $-\frac{1}{2}e^{2} + \frac{3}{2}$
17 $[17, 17, -w^{2} + w + 5]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - \frac{3}{2}$
27 $[27, 3, -w^{3} + 4w - 2]$ $-e^{2} - e + 2$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}\frac{1}{2}e^{2} + e - \frac{9}{2}$
29 $[29, 29, -w^{3} + 4w + 2]$ $-\frac{1}{2}e^{2} - 2e + \frac{3}{2}$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $-e^{2} - 3e + 1$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $-e^{2} - 2e$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $\phantom{-}e^{2} + 4e - 11$
61 $[61, 61, w^{2} - 2w - 2]$ $-e^{2} - 3e + 1$
61 $[61, 61, 2w^{2} - w - 8]$ $-\frac{1}{2}e^{2} - 4e + \frac{11}{2}$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}2e^{2} + 3e - 11$
73 $[73, 73, -w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + 4e - \frac{11}{2}$
79 $[79, 79, w^{2} - 2w - 4]$ $\phantom{-}e^{2} - e - 10$
89 $[89, 89, w^{2} + w - 5]$ $-\frac{1}{2}e^{2} - 3e + \frac{9}{2}$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $-\frac{3}{2}e^{2} - 5e + \frac{15}{2}$
89 $[89, 89, w^{3} - 5w - 5]$ $-e^{2} - e - 3$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $-e^{2} - 5e + 3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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