# Properties

 Base field 3.3.733.1 Weight [2, 2, 2] Level norm 13 Level $[13, 13, w + 1]$ Label 3.3.733.1-13.1-c Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.733.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 7x + 8$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[13, 13, w + 1]$ Label 3.3.733.1-13.1-c Dimension 3 Is CM no Is base change no Parent newspace dimension 11

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 5x$$ $$\mathstrut +\mathstrut 3$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 5]$ $\phantom{-}e^{2} + e - 5$
5 $[5, 5, -w + 3]$ $-e - 1$
7 $[7, 7, -w^{2} - 2w + 3]$ $\phantom{-}e^{2} + e - 5$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}e^{2} + e - 5$
13 $[13, 13, w + 1]$ $-1$
23 $[23, 23, w^{2} - 3]$ $-3e$
25 $[25, 5, w^{2} + 2w - 1]$ $-e^{2} - e + 10$
27 $[27, 3, -3]$ $-3e^{2} - e + 10$
29 $[29, 29, -3w + 7]$ $-2e^{2} + 5$
43 $[43, 43, -3w^{2} - 2w + 17]$ $-e^{2} - 5e + 2$
49 $[49, 7, -2w^{2} + w + 11]$ $-2e^{2} + 8$
67 $[67, 67, -2w^{2} - 4w + 3]$ $\phantom{-}3e^{2} + 7e - 14$
71 $[71, 71, -2w^{2} + w + 9]$ $\phantom{-}4e^{2} + 3e - 17$
73 $[73, 73, w^{2} + 2w - 7]$ $-e^{2} - 2e + 3$
73 $[73, 73, -2w^{2} - 2w + 11]$ $-3e^{2} - 4e + 1$
73 $[73, 73, w - 5]$ $\phantom{-}2e^{2} + 3e - 5$
89 $[89, 89, 2w^{2} + w - 9]$ $-2e$
89 $[89, 89, -w^{2} - 2w + 9]$ $-4e^{2} - e + 6$
89 $[89, 89, -2w - 1]$ $-3e^{2} - 6e + 18$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, w + 1]$ $1$