# Properties

 Label 4.4.13676.1-16.2-f Base field 4.4.13676.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, w^{2} - 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13676.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} + 7x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 4, w^{2} - 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $15$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 3x^{3} - 11x^{2} - 31x - 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 5w + 1]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{9}{4}e + \frac{5}{2}$
11 $[11, 11, -w^{3} + 6w - 2]$ $-e - 1$
13 $[13, 13, -w^{2} + 4]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{13}{4}e + \frac{3}{2}$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{13}{4}e - \frac{11}{2}$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}\frac{3}{4}e^{3} + \frac{3}{2}e^{2} - \frac{31}{4}e - \frac{17}{2}$
37 $[37, 37, -w^{3} + 6w - 4]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{17}{4}e + \frac{1}{2}$
41 $[41, 41, -w^{3} + 5w - 5]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{9}{4}e - \frac{13}{2}$
43 $[43, 43, w^{3} - 4w + 4]$ $-e^{3} - e^{2} + 10e + 10$
43 $[43, 43, -2w^{3} + 11w - 2]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e - 1$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{7}{2}e - 4$
47 $[47, 47, 2w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{9}{2}e - 9$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}e^{3} + e^{2} - 11e - 9$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{13}{2}e + 11$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $\phantom{-}e^{3} + 2e^{2} - 10e - 15$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{17}{2}e + 5$
81 $[81, 3, -3]$ $-\frac{3}{4}e^{3} - \frac{1}{2}e^{2} + \frac{23}{4}e - \frac{5}{2}$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{11}{2}e + 2$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $\phantom{-}\frac{3}{4}e^{3} - \frac{1}{2}e^{2} - \frac{43}{4}e + \frac{5}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $-1$