# Properties

 Base field 4.4.13068.1 Weight [2, 2, 2, 2] Level norm 12 Level $[12, 6, -2w^{3} + 3w^{2} + 11w - 3]$ Label 4.4.13068.1-12.1-i Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13068.1

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

## Form

 Weight [2, 2, 2, 2] Level $[12, 6, -2w^{3} + 3w^{2} + 11w - 3]$ Label 4.4.13068.1-12.1-i Dimension 4 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 58x^{2} + 784$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}\frac{1}{28}e^{3} - \frac{15}{14}e$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $-1$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $-1$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}\frac{1}{28}e^{3} - \frac{29}{14}e$
17 $[17, 17, -w + 2]$ $\phantom{-}e$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}\frac{3}{28}e^{3} - \frac{59}{14}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{8}{7}e$
31 $[31, 31, -w^{2} + 2]$ $\phantom{-}e^{2} - 26$
31 $[31, 31, -w^{3} + 7w + 5]$ $-e^{2} + 32$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $-\frac{1}{14}e^{3} + \frac{8}{7}e$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $-\frac{3}{28}e^{3} + \frac{59}{14}e$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $-e^{2} + 32$
67 $[67, 67, -w^{2} + 4w + 2]$ $\phantom{-}e^{2} - 26$
83 $[83, 83, 2w^{2} - 5w - 2]$ $-\frac{5}{28}e^{3} + \frac{75}{14}e$
83 $[83, 83, -w^{3} + 8w + 6]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{15}{7}e$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $-\frac{5}{28}e^{3} + \frac{75}{14}e$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{15}{7}e$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $\phantom{-}2$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $\phantom{-}2$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $\phantom{-}14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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