# Properties

 Label 4.4.11025.1-16.1-g Base field $$\Q(\sqrt{5}, \sqrt{21})$$ Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change yes

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{5}, \sqrt{21})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 13x^{2} + 16$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 20x^{2} + 72$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{11}{4}w + 5]$ $\phantom{-}1$
4 $[4, 2, \frac{1}{8}w^{3} - \frac{1}{2}w^{2} - \frac{5}{8}w + \frac{3}{2}]$ $\phantom{-}1$
5 $[5, 5, -\frac{3}{8}w^{3} + \frac{35}{8}w - \frac{1}{2}]$ $\phantom{-}e$
5 $[5, 5, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{1}{2}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ $-e^{2} + 10$
41 $[41, 41, \frac{1}{8}w^{3} - \frac{1}{8}w + \frac{3}{2}]$ $-2e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{3}{2}]$ $-2e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{3}{2}]$ $-2e$
41 $[41, 41, -\frac{1}{8}w^{3} + \frac{1}{8}w + \frac{3}{2}]$ $-2e$
49 $[49, 7, \frac{1}{8}w^{3} - \frac{17}{8}w + \frac{7}{2}]$ $\phantom{-}2e^{2} - 22$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w - \frac{5}{2}]$ $\phantom{-}e$
59 $[59, 59, -\frac{7}{8}w^{3} + \frac{3}{2}w^{2} + \frac{83}{8}w - \frac{35}{2}]$ $\phantom{-}e$
59 $[59, 59, -\frac{3}{4}w^{3} + \frac{3}{2}w^{2} + \frac{33}{4}w - 16]$ $\phantom{-}e$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w + \frac{5}{2}]$ $\phantom{-}e$
79 $[79, 79, \frac{3}{8}w^{3} - w^{2} - \frac{35}{8}w + \frac{21}{2}]$ $-e^{2} + 8$
79 $[79, 79, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 5]$ $-e^{2} + 8$
79 $[79, 79, \frac{7}{8}w^{3} - \frac{79}{8}w - \frac{1}{2}]$ $-e^{2} + 8$
79 $[79, 79, -\frac{3}{8}w^{3} - w^{2} + \frac{35}{8}w + \frac{21}{2}]$ $-e^{2} + 8$
89 $[89, 89, \frac{1}{8}w^{3} - \frac{1}{8}w - \frac{5}{2}]$ $\phantom{-}e^{3} - 12e$
89 $[89, 89, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{5}{2}]$ $\phantom{-}e^{3} - 12e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{4}w^{3}-\frac{1}{2}w^{2}-\frac{11}{4}w+5]$ $-1$
$4$ $[4,2,\frac{1}{8}w^{3}-\frac{1}{2}w^{2}-\frac{5}{8}w+\frac{3}{2}]$ $-1$