# Properties

 Base field 4.4.8768.1 Weight [2, 2, 2, 2] Level norm 23 Level $[23,23,w^{3} - 2w^{2} - 2w + 2]$ Label 4.4.8768.1-23.2-a Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8768.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 6x + 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[23,23,w^{3} - 2w^{2} - 2w + 2]$ Label 4.4.8768.1-23.2-a Dimension 4 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut 4x^{3}$$ $$\mathstrut -\mathstrut 9x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w]$ $\phantom{-}e^{3} + 2e^{2} - 2e - 1$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}e^{3} + 2e^{2} - 3e - 3$
7 $[7, 7, w^{2} - 2]$ $-2e^{3} - 4e^{2} + 5e + 1$
7 $[7, 7, w - 1]$ $-e^{2} - 2e + 1$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e^{3} + 4e^{2} + e - 6$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}1$
31 $[31, 31, w^{2} - 5]$ $-e^{3} - e^{2} + 3e$
31 $[31, 31, -w^{2} + 2w + 4]$ $-5e^{3} - 8e^{2} + 17e + 3$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}4e^{3} + 8e^{2} - 11e - 6$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}3e^{3} + 5e^{2} - 6e + 1$
47 $[47, 47, w^{2} - 2w - 5]$ $-5e^{3} - 10e^{2} + 12e + 5$
47 $[47, 47, w^{2} - 6]$ $-3e^{3} - 3e^{2} + 11e - 1$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}7e^{3} + 9e^{2} - 23e + 8$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}e^{3} + 6e^{2} + 2e - 12$
79 $[79, 79, -w - 3]$ $\phantom{-}5e^{3} + 9e^{2} - 13e - 4$
79 $[79, 79, w - 4]$ $-2e^{3} - 4e^{2} + 4e + 5$
81 $[81, 3, -3]$ $\phantom{-}4e^{3} - 23e + 17$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}e^{3} - e^{2} - 11e - 5$
89 $[89, 89, w^{2} + w - 4]$ $-6e^{2} - 13e + 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23,23,w^{3} - 2w^{2} - 2w + 2]$ $-1$