Properties

 Label 4.4.18625.1-16.2-e 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 no 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: no 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:

 $$x^{4} - 10x^{2} + 4$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}0$
4 $[4, 2, w - 3]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $-\frac{1}{2}e^{3} + 5e$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $\phantom{-}\frac{1}{2}e^{3} - 4e$
9 $[9, 3, -w - 2]$ $-\frac{1}{2}e^{3} + 4e$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $\phantom{-}\frac{1}{2}e^{2}$
11 $[11, 11, -w + 2]$ $\phantom{-}\frac{1}{2}e^{2}$
41 $[41, 41, -w]$ $-\frac{3}{2}e^{2} + 13$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $-\frac{1}{2}e^{2} + 5$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $-e^{3} + 7e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $-e$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $\phantom{-}\frac{3}{2}e^{2} - 3$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $\phantom{-}\frac{1}{2}e^{2} - 7$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $\phantom{-}\frac{1}{2}e^{2}$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $\phantom{-}\frac{5}{2}e^{2} - 10$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $-\frac{3}{2}e^{2} + 16$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $\phantom{-}\frac{1}{2}e^{2} - 6$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $-\frac{1}{2}e^{3} + 2e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $\phantom{-}\frac{1}{2}e^{3} - 6e$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $-\frac{5}{2}e^{3} + 25e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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