# Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 13 Level $[13, 13, -w^{2} + w + 4]$ Label 3.3.761.1-13.1-b Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.761.1

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

## Form

 Weight [2, 2, 2] Level $[13, 13, -w^{2} + w + 4]$ Label 3.3.761.1-13.1-b 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:
$$x^{5} + 5x^{4} + 3x^{3} - 13x^{2} - 9x + 8$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}e^{3} + e^{2} - 4e$
8 $[8, 2, 2]$ $-e^{4} - 3e^{3} + 2e^{2} + 7e - 1$
9 $[9, 3, -w^{2} + 2w + 4]$ $-e^{4} - 2e^{3} + 5e^{2} + 6e - 8$
11 $[11, 11, -w^{2} + 2w + 2]$ $-e^{3} - 3e^{2} + 2$
13 $[13, 13, -w^{2} + w + 4]$ $-1$
19 $[19, 19, w + 3]$ $\phantom{-}e^{4} + 3e^{3} + e^{2} - e - 4$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}e^{4} + 2e^{3} - 5e^{2} - 7e + 4$
19 $[19, 19, -w^{2} + 3w + 2]$ $-2e^{3} - 4e^{2} + 4e + 2$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}2e^{4} + 7e^{3} - 3e^{2} - 17e + 2$
23 $[23, 23, -w^{2} + 2]$ $-e^{4} - 2e^{3} + 3e^{2} + 2e - 6$
23 $[23, 23, -w + 4]$ $\phantom{-}2e^{4} + 5e^{3} - 8e^{2} - 12e + 12$
31 $[31, 31, w^{2} - 5]$ $-e^{4} - 5e^{3} - 2e^{2} + 10e$
43 $[43, 43, w^{2} - 3w - 3]$ $\phantom{-}e^{3} + 3e^{2} - e - 2$
49 $[49, 7, w^{2} - 6]$ $-2e^{4} - 5e^{3} + 10e^{2} + 15e - 18$
53 $[53, 53, 2w - 5]$ $-e^{4} - 3e^{3} + e + 2$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-2e^{4} - 3e^{3} + 14e^{2} + 9e - 20$
71 $[71, 71, 2w - 3]$ $\phantom{-}2e^{4} + 9e^{3} + 7e^{2} - 13e - 8$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}3e^{4} + 9e^{3} - 3e^{2} - 13e$
83 $[83, 83, w^{2} - w - 9]$ $-4e^{4} - 9e^{3} + 13e^{2} + 16e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{2} + w + 4]$ $1$