# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 23 Level $[23, 23, -w^{3} + 4w + 2]$ Label 4.4.16997.1-23.1-d Dimension 24 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16997.1

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

## Form

 Weight [2, 2, 2, 2] Level $[23, 23, -w^{3} + 4w + 2]$ Label 4.4.16997.1-23.1-d Dimension 24 Is CM no Is base change no Parent newspace dimension 39

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{24} - 2x^{23} - 66x^{22} + 122x^{21} + 1836x^{20} - 3075x^{19} - 28260x^{18} + 42046x^{17} + 264773x^{16} - 342282x^{15} - 1563094x^{14} + 1702865x^{13} + 5824627x^{12} - 5068915x^{11} - 13388400x^{10} + 8333030x^{9} + 18039920x^{8} - 6198892x^{7} - 12772392x^{6} + 1007336x^{5} + 3505028x^{4} + 84140x^{3} - 249688x^{2} + 14968x - 184$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 2]$ $...$
7 $[7, 7, -w^{2} + 2]$ $...$
13 $[13, 13, -w^{2} + 3]$ $...$
13 $[13, 13, w^{2} - w - 4]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -w^{2} + w + 1]$ $...$
23 $[23, 23, -w^{3} + 4w + 2]$ $-1$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $...$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $...$
29 $[29, 29, -w + 3]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $...$
37 $[37, 37, w^{3} - 4w - 1]$ $...$
37 $[37, 37, w^{3} - 3w + 1]$ $...$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $...$
59 $[59, 59, w^{2} + w - 4]$ $...$
61 $[61, 61, -2w^{2} + w + 8]$ $...$
73 $[73, 73, -w^{3} + 5w - 1]$ $...$
79 $[79, 79, 2w^{2} + w - 6]$ $...$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23, 23, -w^{3} + 4w + 2]$ $1$