# Properties

 Label 4.4.16609.1-3.1-a Base field 4.4.16609.1 Weight $[2, 2, 2, 2]$ Level norm $3$ Level $[3, 3, -w^{2} + w + 3]$ Dimension $1$ CM no Base change no

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## Base field 4.4.16609.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} - x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[3, 3, -w^{2} + w + 3]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $3$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}1$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}1$
5 $[5, 5, w^{2} - 4]$ $\phantom{-}1$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $-5$
17 $[17, 17, -w^{2} + w + 5]$ $-1$
27 $[27, 3, -w^{3} + 4w - 2]$ $-2$
29 $[29, 29, -w^{2} + w + 1]$ $-3$
29 $[29, 29, -w^{3} + 4w + 2]$ $-3$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $-3$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $\phantom{-}5$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $-6$
61 $[61, 61, w^{2} - 2w - 2]$ $\phantom{-}5$
61 $[61, 61, 2w^{2} - w - 8]$ $-13$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}4$
73 $[73, 73, -w^{2} - 2w + 2]$ $-11$
79 $[79, 79, w^{2} - 2w - 4]$ $-4$
89 $[89, 89, w^{2} + w - 5]$ $-11$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $-3$
89 $[89, 89, w^{3} - 5w - 5]$ $-5$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $-7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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