# Properties

 Label 4.4.17069.1-17.3-d Base field 4.4.17069.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17,17,w^{3} - 3w^{2} - 2w + 2]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17069.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} - 4x + 3$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17,17,w^{3} - 3w^{2} - 2w + 2]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $37$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 2x^{2} - 2x - 2$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $-e - 1$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $-e^{2} - 2e + 1$
16 $[16, 2, 2]$ $-e^{2} - 2e + 3$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $\phantom{-}3$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $-2e^{2} - e + 5$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}1$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}e^{2} + 2e - 3$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $-2e^{2} - 5e + 1$
25 $[25, 5, w^{2} - 2w - 7]$ $-3e^{2} - 3e + 6$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $\phantom{-}3e^{2} + 2e - 9$
29 $[29, 29, w - 2]$ $\phantom{-}2e^{2} + 2e$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}2e^{2} + 2e - 11$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $-2e^{2} + e + 2$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $-2e^{2} - 6e + 2$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $\phantom{-}5e^{2} + 7e - 12$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $\phantom{-}6e^{2} + 7e - 12$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}4e - 2$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $\phantom{-}6e^{2} + 11e - 10$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}e^{2} + 3e - 13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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