# Properties

 Label 4.4.18625.1-16.3-f Base field 4.4.18625.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16,4,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{2}{3}]$ Dimension $12$ 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: $[16,4,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{2}{3}]$ Dimension: $12$ 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:

 $$x^{12} - 33x^{10} + 408x^{8} - 2323x^{6} + 6021x^{4} - 6150x^{2} + 1156$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}e$
4 $[4, 2, w - 3]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $-\frac{61}{918}e^{11} + \frac{1537}{918}e^{9} - \frac{385}{27}e^{7} + \frac{43817}{918}e^{5} - \frac{52679}{918}e^{3} + \frac{4366}{459}e$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $-\frac{26}{153}e^{11} + \frac{1291}{306}e^{9} - \frac{316}{9}e^{7} + \frac{17422}{153}e^{5} - \frac{42197}{306}e^{3} + \frac{5557}{153}e$
9 $[9, 3, -w - 2]$ $-\frac{4}{459}e^{11} + \frac{179}{918}e^{9} - \frac{35}{27}e^{7} + \frac{962}{459}e^{5} + \frac{1421}{918}e^{3} - \frac{67}{459}e$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $\phantom{-}\frac{11}{54}e^{10} - \frac{263}{54}e^{8} + \frac{1024}{27}e^{6} - \frac{5845}{54}e^{4} + \frac{5839}{54}e^{2} - \frac{539}{27}$
11 $[11, 11, -w + 2]$ $-\frac{7}{54}e^{10} + \frac{169}{54}e^{8} - \frac{668}{27}e^{6} + \frac{3911}{54}e^{4} - \frac{4043}{54}e^{2} + \frac{469}{27}$
41 $[41, 41, -w]$ $\phantom{-}\frac{2}{3}e^{10} - \frac{33}{2}e^{8} + \frac{409}{3}e^{6} - \frac{1300}{3}e^{4} + \frac{983}{2}e^{2} - \frac{260}{3}$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $\phantom{-}\frac{5}{9}e^{10} - \frac{247}{18}e^{8} + \frac{1019}{9}e^{6} - \frac{3250}{9}e^{4} + \frac{7583}{18}e^{2} - \frac{766}{9}$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $\phantom{-}\frac{19}{459}e^{11} - \frac{559}{459}e^{9} + \frac{344}{27}e^{7} - \frac{25454}{459}e^{5} + \frac{39293}{459}e^{3} - \frac{9971}{459}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $-\frac{13}{459}e^{11} + \frac{310}{459}e^{9} - \frac{143}{27}e^{7} + \frac{7487}{459}e^{5} - \frac{11786}{459}e^{3} + \frac{12137}{459}e$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $\phantom{-}\frac{31}{54}e^{10} - \frac{769}{54}e^{8} + \frac{3191}{27}e^{6} - \frac{20483}{54}e^{4} + \frac{23747}{54}e^{2} - \frac{2122}{27}$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $-\frac{53}{54}e^{10} + \frac{1295}{54}e^{8} - \frac{5239}{27}e^{6} + \frac{32173}{54}e^{4} - \frac{35425}{54}e^{2} + \frac{3416}{27}$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $-\frac{22}{27}e^{10} + \frac{1079}{54}e^{8} - \frac{4393}{27}e^{6} + \frac{13661}{27}e^{4} - \frac{30673}{54}e^{2} + \frac{2831}{27}$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $\phantom{-}\frac{20}{27}e^{10} - \frac{985}{54}e^{8} + \frac{4037}{27}e^{6} - \frac{12694}{27}e^{4} + \frac{28877}{54}e^{2} - \frac{2653}{27}$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $-\frac{13}{18}e^{10} + \frac{319}{18}e^{8} - \frac{1301}{9}e^{6} + \frac{8135}{18}e^{4} - \frac{9329}{18}e^{2} + \frac{1033}{9}$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $-\frac{35}{54}e^{10} + \frac{863}{54}e^{8} - \frac{3547}{27}e^{6} + \frac{22471}{54}e^{4} - \frac{26083}{54}e^{2} + \frac{2543}{27}$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $-\frac{215}{918}e^{11} + \frac{5327}{918}e^{9} - \frac{1295}{27}e^{7} + \frac{139147}{918}e^{5} - \frac{149599}{918}e^{3} + \frac{2273}{459}e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $\phantom{-}\frac{235}{918}e^{11} - \frac{5851}{918}e^{9} + \frac{1441}{27}e^{7} - \frac{161399}{918}e^{5} + \frac{204263}{918}e^{3} - \frac{31405}{459}e$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $-\frac{4}{51}e^{11} + \frac{71}{34}e^{9} - \frac{58}{3}e^{7} + \frac{3767}{51}e^{5} - \frac{3697}{34}e^{3} + \frac{1990}{51}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w - 3]$ $1$