# Properties

 Label 4.4.14400.1-9.1-d Base field $$\Q(\sqrt{5}, \sqrt{6})$$ Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ Dimension $2$ CM no Base change no

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## Base field $$\Q(\sqrt{5}, \sqrt{6})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 13x^{2} + 14x + 19$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 8$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $\phantom{-}0$
5 $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $\phantom{-}e$
5 $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ $-e$
9 $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $\phantom{-}1$
19 $[19, 19, -w]$ $-2e - 2$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ $\phantom{-}2e - 2$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ $-2e - 2$
19 $[19, 19, w - 1]$ $\phantom{-}2e - 2$
29 $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ $-e - 4$
29 $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ $-e + 4$
29 $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ $\phantom{-}e + 4$
29 $[29, 29, -w + 3]$ $\phantom{-}e - 4$
49 $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ $-6$
49 $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ $-6$
71 $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ $\phantom{-}4e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ $\phantom{-}4e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ $-4e$
71 $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ $-4e$
101 $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ $-e - 12$
101 $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ $\phantom{-}e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $-1$