# Properties

 Label 4.4.17069.1-9.4-a Base field 4.4.17069.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9,9,w - 1]$ Dimension $1$ CM no Base change no

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## 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: $[9,9,w - 1]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}0$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $\phantom{-}2$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $-3$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}0$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}6$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $-2$
25 $[25, 5, w^{2} - 2w - 7]$ $-7$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $-6$
29 $[29, 29, w - 2]$ $-9$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $-12$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $\phantom{-}9$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $-7$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $-8$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $-12$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $-8$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $\phantom{-}4$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $-3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3,3,w^{3} - 2w^{2} - 6w + 1]$ $-1$