# Properties

 Label 4.4.4225.1-36.4-d Base field $$\Q(\sqrt{5}, \sqrt{13})$$ Weight $[2, 2, 2, 2]$ Level norm $36$ Level $[36,6,-\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{5}, \sqrt{13})$$

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[36,6,-\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $7$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} - x^{2} - 7x - 1$$
Norm Prime Eigenvalue
4 $[4, 2, w]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{9}{2}w]$ $\phantom{-}1$
9 $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w - \frac{1}{2}]$ $\phantom{-}e^{2} - 2e - 5$
9 $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w + \frac{1}{2}]$ $\phantom{-}1$
25 $[25, 5, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-e - 1$
29 $[29, 29, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w - \frac{1}{2}]$ $-e^{2} + 3e + 8$
29 $[29, 29, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ $-e + 3$
29 $[29, 29, -\frac{1}{2}w^{2} + \frac{1}{2}w + 4]$ $-2e^{2} + 2e + 6$
29 $[29, 29, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ $\phantom{-}2e^{2} - 2e - 10$
49 $[49, 7, \frac{3}{4}w^{3} + \frac{1}{2}w^{2} - \frac{23}{4}w - \frac{3}{2}]$ $\phantom{-}3e + 3$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ $-e^{2} + 11$
61 $[61, 61, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 1]$ $-2$
61 $[61, 61, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{13}{4}w + \frac{7}{2}]$ $-e^{2} + 4e + 3$
61 $[61, 61, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{13}{4}w - \frac{7}{2}]$ $-2e^{2} + e + 11$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 1]$ $-2$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{25}{4}w - \frac{9}{2}]$ $\phantom{-}2e^{2} + e - 7$
79 $[79, 79, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{3}{4}w - \frac{3}{2}]$ $-3e - 1$
79 $[79, 79, \frac{1}{4}w^{3} - \frac{3}{4}w - \frac{9}{2}]$ $-3e^{2} + 2e + 17$
79 $[79, 79, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 13w - 3]$ $-2e^{2} - 2e + 12$
101 $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{7}{4}w - \frac{5}{2}]$ $\phantom{-}3e^{2} - 4e - 17$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{2}w^{3} - \frac{9}{2}w]$ $-1$
$9$ $[9,3,-\frac{1}{4}w^{3} + \frac{11}{4}w - \frac{1}{2}]$ $-1$