# Properties

 Label 4.4.6809.1-23.1-d Base field 4.4.6809.1 Weight $[2, 2, 2, 2]$ Level norm $23$ Level $[23, 23, -w^{2} + 2]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.6809.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[23, 23, -w^{2} + 2]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $13$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{3} - 3x + 1$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 4w]$ $-1$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $\phantom{-}2e^{2} - 2$
11 $[11, 11, w^{3} - 5w + 1]$ $-3e^{2} - 2e + 5$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $-e^{2} - e - 2$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}1$
29 $[29, 29, -w^{2} - w + 3]$ $\phantom{-}3e^{2} + 2e - 11$
31 $[31, 31, -w^{3} + 6w + 2]$ $\phantom{-}e^{2} + 5e - 3$
43 $[43, 43, w^{3} - 6w]$ $-4e^{2} + e + 11$
47 $[47, 47, 2w^{3} - 9w]$ $\phantom{-}e^{2} - 5e - 1$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $-2e^{2} + 3e + 3$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $\phantom{-}e^{2} + 2e - 3$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}e^{2} + e - 13$
59 $[59, 59, 3w^{3} - 15w - 5]$ $-5e^{2} - 3e + 8$
71 $[71, 71, w^{3} - 3w - 3]$ $\phantom{-}6e^{2} - e - 15$
81 $[81, 3, -3]$ $-2e^{2} + e + 8$
83 $[83, 83, -2w^{3} + 8w + 3]$ $\phantom{-}4e^{2} + 5e - 8$
89 $[89, 89, -2w^{3} + 11w - 2]$ $\phantom{-}e^{2} + 2e - 2$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $-3e + 1$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $-6e^{2} - 5e + 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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