# Properties

 Base field 4.4.18625.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.18625.1-16.1-c Dimension 11 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.18625.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 14x^{2} + 9x + 41$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.18625.1-16.1-c Dimension 11 Is CM no Is base change yes Parent newspace dimension 30

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{11}$$ $$\mathstrut -\mathstrut x^{10}$$ $$\mathstrut -\mathstrut 53x^{9}$$ $$\mathstrut +\mathstrut 46x^{8}$$ $$\mathstrut +\mathstrut 1006x^{7}$$ $$\mathstrut -\mathstrut 720x^{6}$$ $$\mathstrut -\mathstrut 8252x^{5}$$ $$\mathstrut +\mathstrut 4144x^{4}$$ $$\mathstrut +\mathstrut 28752x^{3}$$ $$\mathstrut -\mathstrut 3520x^{2}$$ $$\mathstrut -\mathstrut 35840x$$ $$\mathstrut -\mathstrut 15360$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}1$
4 $[4, 2, w - 3]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $...$
9 $[9, 3, -w - 2]$ $...$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $...$
11 $[11, 11, -w + 2]$ $...$
41 $[41, 41, -w]$ $...$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $...$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $...$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $...$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $...$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $...$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $...$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $...$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $...$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $...$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $...$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $-1$
4 $[4, 2, w - 3]$ $-1$