# Properties

 Label 4.4.18625.1-16.2-c Base field 4.4.18625.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{5}{6}]$ Dimension $4$ CM yes Base change no

# 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: $[16, 4, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{5}{6}]$ Dimension: $4$ CM: yes Base change: no Newspace dimension: $28$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 4x^{3} - 39x^{2} - 176x - 139$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}0$
4 $[4, 2, w - 3]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $\phantom{-}0$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $\phantom{-}0$
9 $[9, 3, -w - 2]$ $\phantom{-}0$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $\phantom{-}e$
11 $[11, 11, -w + 2]$ $-\frac{8}{61}e^{3} - \frac{13}{61}e^{2} + \frac{320}{61}e + \frac{709}{61}$
41 $[41, 41, -w]$ $-\frac{3}{61}e^{3} + \frac{18}{61}e^{2} + \frac{59}{61}e - \frac{428}{61}$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $\phantom{-}\frac{17}{61}e^{3} + \frac{20}{61}e^{2} - \frac{741}{61}e - \frac{1560}{61}$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $\phantom{-}0$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $\phantom{-}0$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $\phantom{-}\frac{6}{61}e^{3} + \frac{25}{61}e^{2} - \frac{362}{61}e - \frac{852}{61}$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $-\frac{6}{61}e^{3} - \frac{25}{61}e^{2} + \frac{118}{61}e + \frac{1096}{61}$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $\phantom{-}\frac{18}{61}e^{3} + \frac{14}{61}e^{2} - \frac{781}{61}e - \frac{1458}{61}$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $\phantom{-}\frac{18}{61}e^{3} + \frac{14}{61}e^{2} - \frac{659}{61}e - \frac{726}{61}$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $-\frac{4}{61}e^{3} - \frac{37}{61}e^{2} + \frac{282}{61}e + \frac{1239}{61}$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $-\frac{18}{61}e^{3} - \frac{14}{61}e^{2} + \frac{659}{61}e + \frac{1214}{61}$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $\phantom{-}0$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $\phantom{-}0$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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