# Properties

 Base field 3.3.1101.1 Weight [2, 2, 2] Level norm 9 Level $[9, 3, -w^{2} + 9]$ Label 3.3.1101.1-9.1-c Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1101.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 9x + 12$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[9, 3, -w^{2} + 9]$ Label 3.3.1101.1-9.1-c Dimension 5 Is CM no Is base change no Parent newspace dimension 10

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5}$$ $$\mathstrut -\mathstrut 2x^{4}$$ $$\mathstrut -\mathstrut 6x^{3}$$ $$\mathstrut +\mathstrut 10x^{2}$$ $$\mathstrut +\mathstrut 8x$$ $$\mathstrut -\mathstrut 7$$
Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}e^{4} - 6e^{2} - e + 6$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}e^{4} - e^{3} - 5e^{2} + 3e + 3$
19 $[19, 19, w + 1]$ $\phantom{-}2e^{4} + 2e^{3} - 12e^{2} - 10e + 6$
23 $[23, 23, w^{2} - 2w - 1]$ $-e^{3} + 3e^{2} + 2e - 8$
31 $[31, 31, -2w^{2} + 19]$ $\phantom{-}4e^{2} - 2e - 10$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}2e^{4} - 10e^{2}$
31 $[31, 31, -3w + 5]$ $\phantom{-}2e^{4} - e^{3} - 9e^{2} + 4$
41 $[41, 41, w^{2} + 2w - 7]$ $\phantom{-}2e^{4} - 12e^{2} - 2e + 14$
43 $[43, 43, w^{2} - 11]$ $-4e^{3} + 2e^{2} + 16e - 2$
47 $[47, 47, 3w - 7]$ $-2e^{4} - 2e^{3} + 10e^{2} + 8e + 2$
53 $[53, 53, -3w^{2} - 6w + 11]$ $-2e^{4} + 12e^{2} + 4e - 12$
59 $[59, 59, 2w - 1]$ $\phantom{-}3e^{3} - 3e^{2} - 10e + 10$
67 $[67, 67, 2w^{2} + w - 19]$ $-e^{4} + 2e^{3} + 4e^{2} - 7e + 2$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-2e^{2} - 2e + 8$
67 $[67, 67, w - 5]$ $-2e^{4} + 12e^{2} - 14$
73 $[73, 73, -4w^{2} - 3w + 29]$ $-4e^{4} + 2e^{3} + 18e^{2} - 4e - 6$
73 $[73, 73, 2w^{2} - w - 11]$ $-6e^{4} + 2e^{3} + 32e^{2} - 4e - 22$
73 $[73, 73, w^{2} + 2w - 11]$ $-4e^{4} - 3e^{3} + 23e^{2} + 18e - 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-1$