# Properties

 Label 4.4.12725.1-16.1-c Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 28x^{2} + 128$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}\frac{1}{16}e^{3} + \frac{1}{4}e^{2} - \frac{3}{4}e - 4$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $-e$
11 $[11, 11, w - 2]$ $-\frac{1}{16}e^{3} + \frac{1}{4}e^{2} + \frac{3}{4}e - 4$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, w^{2} - 2w - 5]$ $-\frac{1}{4}e^{2} - e + 4$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{4}e^{2} + e + 4$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}\frac{1}{4}e^{2} - 8$
29 $[29, 29, w]$ $\phantom{-}\frac{1}{16}e^{3} - \frac{3}{4}e - 1$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}\frac{3}{16}e^{3} - \frac{1}{2}e^{2} - \frac{17}{4}e + 5$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-\frac{3}{16}e^{3} - \frac{1}{2}e^{2} + \frac{17}{4}e + 5$
29 $[29, 29, w - 1]$ $-\frac{1}{16}e^{3} + \frac{3}{4}e - 1$
31 $[31, 31, w^{3} - 6w - 6]$ $-\frac{3}{16}e^{3} - \frac{1}{2}e^{2} + \frac{17}{4}e + 2$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}\frac{3}{16}e^{3} - \frac{1}{2}e^{2} - \frac{17}{4}e + 2$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $\phantom{-}\frac{1}{4}e^{2} - e - 1$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $\phantom{-}\frac{1}{4}e^{2} + e - 1$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-\frac{1}{16}e^{3} + \frac{1}{2}e^{2} + \frac{11}{4}e - 4$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{1}{16}e^{3} + \frac{1}{2}e^{2} - \frac{11}{4}e - 4$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{1}{16}e^{3} + \frac{3}{4}e^{2} - \frac{3}{4}e - 13$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{1}{16}e^{3} + \frac{3}{4}e^{2} + \frac{3}{4}e - 13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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