# Properties

 Label 4.4.15188.1-16.2-a Base field 4.4.15188.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, w^{2} + w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.15188.1

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

## Form

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

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 6x^{3} - 39x^{2} - 144x - 108$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ $\phantom{-}0$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $-\frac{2}{9}e^{3} - e^{2} + \frac{32}{3}e + 16$
11 $[11, 11, -w^{3} + w^{2} + 6w + 1]$ $-\frac{2}{9}e^{3} - e^{2} + \frac{29}{3}e + 16$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-\frac{1}{18}e^{3} - \frac{1}{6}e^{2} + \frac{8}{3}e + 2$
19 $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ $-\frac{5}{18}e^{3} - \frac{7}{6}e^{2} + \frac{37}{3}e + 18$
23 $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ $\phantom{-}\frac{2}{9}e^{3} + e^{2} - \frac{32}{3}e - 16$
31 $[31, 31, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{3}e^{3} - \frac{5}{3}e^{2} + 14e + 28$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - 15e - 20$
43 $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ $-\frac{1}{18}e^{3} - \frac{1}{6}e^{2} + \frac{8}{3}e + 2$
67 $[67, 67, w^{2} - w - 5]$ $-\frac{2}{3}e^{3} - 3e^{2} + 32e + 56$
67 $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - 15e - 20$
73 $[73, 73, w^{2} + w + 1]$ $\phantom{-}2$
79 $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ $\phantom{-}\frac{4}{9}e^{3} + 2e^{2} - \frac{64}{3}e - 36$
81 $[81, 3, -3]$ $-\frac{2}{9}e^{3} - e^{2} + \frac{32}{3}e + 26$
83 $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ $\phantom{-}\frac{5}{18}e^{3} + \frac{3}{2}e^{2} - \frac{34}{3}e - 26$
83 $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}\frac{2}{9}e^{3} + e^{2} - \frac{32}{3}e - 16$
89 $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ $-\frac{1}{9}e^{3} - e^{2} + \frac{10}{3}e + 20$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{19}{3}e + 4$
97 $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ $-\frac{4}{9}e^{3} - 2e^{2} + \frac{64}{3}e + 34$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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