# Properties

 Label 4.4.8789.1-17.2-e Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17, 17, -w^{3} + w^{2} + 5w]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17, 17, -w^{3} + w^{2} + 5w]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 3x^{3} - 9x^{2} - 32x - 22$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-e^{3} - 2e^{2} + 12e + 20$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}e^{3} + 2e^{2} - 12e - 18$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $\phantom{-}e^{3} + e^{2} - 12e - 14$
16 $[16, 2, 2]$ $-e^{2} + 9$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-e^{3} - 2e^{2} + 12e + 22$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-1$
17 $[17, 17, -w^{2} + 2w + 1]$ $-e^{3} - 2e^{2} + 12e + 22$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}e^{3} + 2e^{2} - 10e - 18$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}2$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}2e^{3} + 2e^{2} - 21e - 22$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}3e^{3} + 5e^{2} - 34e - 48$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}3e^{3} + 4e^{2} - 31e - 42$
47 $[47, 47, w^{3} - 7w - 4]$ $-e^{3} - e^{2} + 10e + 4$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}e^{3} + e^{2} - 12e - 8$
61 $[61, 61, -w - 3]$ $-2e^{3} - 4e^{2} + 24e + 40$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}e^{2} - e - 14$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}4e^{3} + 6e^{2} - 44e - 68$
81 $[81, 3, -3]$ $-e^{3} - 3e^{2} + 12e + 26$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-5e^{3} - 8e^{2} + 57e + 80$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{3} + w^{2} + 5w]$ $1$