# Properties

 Label 4.4.19525.1-16.1-g Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $20$ CM no Base change yes

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $20$ CM: no Base change: yes Newspace dimension: $36$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{20} - 51x^{18} + 1062x^{16} - 11827x^{14} + 77114x^{12} - 302231x^{10} + 704305x^{8} - 936324x^{6} + 653168x^{4} - 198528x^{2} + 12800$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
9 $[9, 3, -w + 3]$ $...$
9 $[9, 3, w + 2]$ $...$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $...$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $...$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $...$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $...$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $...$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $...$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $...$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $...$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $...$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $...$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $...$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $...$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $...$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $...$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$