# Properties

 Label 3.3.785.1-23.3-c Base field 3.3.785.1 Weight $[2, 2, 2]$ Level norm $23$ Level $[23, 23, -w^{2} + 8]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.785.1

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

## Form

 Weight: $[2, 2, 2]$ Level: $[23, 23, -w^{2} + 8]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $23$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{5} + 3x^{4} - 6x^{3} - 23x^{2} - 11x + 7$$
Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $-e^{4} - e^{3} + 8e^{2} + 8e - 3$
5 $[5, 5, -w + 3]$ $-e - 1$
8 $[8, 2, 2]$ $-e - 1$
9 $[9, 3, w^{2} + w - 4]$ $\phantom{-}2e^{4} + 3e^{3} - 16e^{2} - 21e + 7$
13 $[13, 13, w + 3]$ $-e^{2} + 2$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}e^{4} + e^{3} - 8e^{2} - 9e + 2$
23 $[23, 23, w^{2} - 2]$ $-e^{3} - e^{2} + 8e + 5$
23 $[23, 23, w^{2} - 3]$ $-3e^{4} - 5e^{3} + 24e^{2} + 34e - 10$
23 $[23, 23, -w^{2} + 8]$ $-1$
29 $[29, 29, w - 4]$ $\phantom{-}e^{4} + e^{3} - 9e^{2} - 6e + 6$
37 $[37, 37, w^{2} + w - 8]$ $\phantom{-}2e^{4} + 3e^{3} - 16e^{2} - 22e$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}e^{4} - 8e^{2} + 10$
47 $[47, 47, 2w^{2} + w - 8]$ $-4e^{4} - 5e^{3} + 33e^{2} + 37e - 21$
59 $[59, 59, -2w^{2} - 3w + 6]$ $\phantom{-}3e^{4} + 3e^{3} - 25e^{2} - 24e + 16$
61 $[61, 61, -2w - 1]$ $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 14e - 1$
67 $[67, 67, -2w - 3]$ $\phantom{-}2e^{3} + 2e^{2} - 12e - 10$
79 $[79, 79, 2w^{2} - 9]$ $-e^{4} - 2e^{3} + 8e^{2} + 16e + 5$
109 $[109, 109, w^{2} + 2w - 6]$ $\phantom{-}4e^{4} + 6e^{3} - 30e^{2} - 47e + 4$
109 $[109, 109, 2w^{2} + w - 14]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{2} + 8]$ $1$