# Properties

 Label 4.4.13768.1-16.2-c Base field 4.4.13768.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, w^{2} - w - 3]$ Dimension $11$ CM no Base change no

# Related objects

• L-function not available

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## Base field 4.4.13768.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 5x^{2} + 2x + 2$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 4, w^{2} - w - 3]$ Dimension: $11$ CM: no Base change: no Newspace dimension: $21$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{11} - x^{10} - 15x^{9} + 15x^{8} + 74x^{7} - 69x^{6} - 141x^{5} + 114x^{4} + 89x^{3} - 60x^{2} - 12x + 4$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-\frac{61}{163}e^{10} + \frac{8}{163}e^{9} + \frac{946}{163}e^{8} - \frac{61}{163}e^{7} - \frac{4893}{163}e^{6} - \frac{387}{163}e^{5} + \frac{9689}{163}e^{4} + \frac{2453}{163}e^{3} - \frac{5561}{163}e^{2} - \frac{1650}{163}e + \frac{410}{163}$
4 $[4, 2, -w^{2} - w + 1]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{92}{163}e^{10} + \frac{20}{163}e^{9} - \frac{1384}{163}e^{8} - \frac{234}{163}e^{7} + \frac{6920}{163}e^{6} + \frac{1233}{163}e^{5} - \frac{13186}{163}e^{4} - \frac{2914}{163}e^{3} + \frac{7369}{163}e^{2} + \frac{1417}{163}e - \frac{442}{163}$
17 $[17, 17, -w + 3]$ $-\frac{117}{163}e^{10} + \frac{10}{163}e^{9} + \frac{1753}{163}e^{8} - \frac{117}{163}e^{7} - \frac{8602}{163}e^{6} - \frac{280}{163}e^{5} + \frac{15575}{163}e^{4} + \frac{2944}{163}e^{3} - \frac{7155}{163}e^{2} - \frac{2307}{163}e - \frac{58}{163}$
27 $[27, 3, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}\frac{223}{163}e^{10} - \frac{72}{163}e^{9} - \frac{3298}{163}e^{8} + \frac{1201}{163}e^{7} + \frac{16001}{163}e^{6} - \frac{5482}{163}e^{5} - \frac{29336}{163}e^{4} + \frac{8078}{163}e^{3} + \frac{15982}{163}e^{2} - \frac{3406}{163}e - \frac{756}{163}$
31 $[31, 31, -w^{2} - 2w + 1]$ $\phantom{-}\frac{32}{163}e^{10} - \frac{71}{163}e^{9} - \frac{531}{163}e^{8} + \frac{1010}{163}e^{7} + \frac{2981}{163}e^{6} - \frac{4532}{163}e^{5} - \frac{6670}{163}e^{4} + \frac{7427}{163}e^{3} + \frac{4753}{163}e^{2} - \frac{3816}{163}e - \frac{338}{163}$
41 $[41, 41, -w^{2} + 5]$ $-\frac{275}{163}e^{10} + \frac{4}{163}e^{9} + \frac{4222}{163}e^{8} - \frac{112}{163}e^{7} - \frac{21762}{163}e^{6} - \frac{438}{163}e^{5} + \frac{43883}{163}e^{4} + \frac{3753}{163}e^{3} - \frac{28290}{163}e^{2} - \frac{1803}{163}e + \frac{2976}{163}$
43 $[43, 43, w^{3} - w^{2} - 5w - 1]$ $\phantom{-}\frac{274}{163}e^{10} - \frac{68}{163}e^{9} - \frac{4129}{163}e^{8} + \frac{926}{163}e^{7} + \frac{20482}{163}e^{6} - \frac{2497}{163}e^{5} - \frac{38265}{163}e^{4} - \frac{1209}{163}e^{3} + \frac{20292}{163}e^{2} + \frac{2778}{163}e - \frac{1040}{163}$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $-\frac{345}{163}e^{10} + \frac{88}{163}e^{9} + \frac{5190}{163}e^{8} - \frac{1323}{163}e^{7} - \frac{25787}{163}e^{6} + \frac{4708}{163}e^{5} + \frac{48877}{163}e^{4} - \frac{3335}{163}e^{3} - \frac{28082}{163}e^{2} + \frac{1410}{163}e + \frac{2228}{163}$
59 $[59, 59, -w - 3]$ $-\frac{27}{163}e^{10} - \frac{98}{163}e^{9} + \frac{392}{163}e^{8} + \frac{1440}{163}e^{7} - \frac{1797}{163}e^{6} - \frac{7036}{163}e^{5} + \frac{2215}{163}e^{4} + \frac{12942}{163}e^{3} + \frac{1659}{163}e^{2} - \frac{6438}{163}e - \frac{866}{163}$
59 $[59, 59, -2w^{3} + 2w^{2} + 9w - 5]$ $-\frac{177}{163}e^{10} - \frac{81}{163}e^{9} + \frac{2769}{163}e^{8} + \frac{1290}{163}e^{7} - \frac{14660}{163}e^{6} - \frac{7675}{163}e^{5} + \frac{30241}{163}e^{4} + \frac{17360}{163}e^{3} - \frac{18410}{163}e^{2} - \frac{8518}{163}e + \frac{1024}{163}$
59 $[59, 59, -w^{3} - 3w^{2} - w + 3]$ $-\frac{142}{163}e^{10} + \frac{40}{163}e^{9} + \frac{2122}{163}e^{8} - \frac{631}{163}e^{7} - \frac{10447}{163}e^{6} + \frac{2466}{163}e^{5} + \frac{19594}{163}e^{4} - \frac{1916}{163}e^{3} - \frac{11342}{163}e^{2} - \frac{752}{163}e + \frac{1072}{163}$
59 $[59, 59, w^{3} - 7w + 1]$ $-\frac{172}{163}e^{10} + \frac{76}{163}e^{9} + \frac{2630}{163}e^{8} - \frac{1150}{163}e^{7} - \frac{13313}{163}e^{6} + \frac{5044}{163}e^{5} + \frac{25623}{163}e^{4} - \frac{7911}{163}e^{3} - \frac{14606}{163}e^{2} + \frac{5026}{163}e + \frac{1776}{163}$
61 $[61, 61, -w^{3} + w^{2} + 2w + 5]$ $\phantom{-}\frac{218}{163}e^{10} - \frac{66}{163}e^{9} - \frac{3159}{163}e^{8} + \frac{1033}{163}e^{7} + \frac{14817}{163}e^{6} - \frac{4020}{163}e^{5} - \frac{25696}{163}e^{4} + \frac{3683}{163}e^{3} + \frac{12667}{163}e^{2} + \frac{2}{163}e - \frac{530}{163}$
61 $[61, 61, -w^{3} - w^{2} + 4w + 3]$ $\phantom{-}\frac{81}{163}e^{10} - \frac{32}{163}e^{9} - \frac{1176}{163}e^{8} + \frac{407}{163}e^{7} + \frac{5554}{163}e^{6} - \frac{1060}{163}e^{5} - \frac{9905}{163}e^{4} - \frac{195}{163}e^{3} + \frac{5292}{163}e^{2} - \frac{83}{163}e - \frac{336}{163}$
67 $[67, 67, 4w^{3} - 4w^{2} - 18w + 7]$ $\phantom{-}\frac{135}{163}e^{10} + \frac{1}{163}e^{9} - \frac{2123}{163}e^{8} - \frac{28}{163}e^{7} + \frac{11267}{163}e^{6} + \frac{950}{163}e^{5} - \frac{23300}{163}e^{4} - \frac{4400}{163}e^{3} + \frac{14688}{163}e^{2} + \frac{3176}{163}e - \frac{560}{163}$
73 $[73, 73, -2w^{3} + 6w - 3]$ $-\frac{264}{163}e^{10} + \frac{219}{163}e^{9} + \frac{3851}{163}e^{8} - \frac{3198}{163}e^{7} - \frac{18114}{163}e^{6} + \frac{13591}{163}e^{5} + \frac{31474}{163}e^{4} - \frac{18852}{163}e^{3} - \frac{15618}{163}e^{2} + \frac{7684}{163}e + \frac{1566}{163}$
73 $[73, 73, -2w + 3]$ $\phantom{-}\frac{157}{163}e^{10} - \frac{58}{163}e^{9} - \frac{2376}{163}e^{8} + \frac{809}{163}e^{7} + \frac{11880}{163}e^{6} - \frac{2777}{163}e^{5} - \frac{22527}{163}e^{4} + \frac{1898}{163}e^{3} + \frac{11996}{163}e^{2} - \frac{833}{163}e - \frac{120}{163}$
97 $[97, 97, w^{3} - 2w^{2} - 5w + 3]$ $-\frac{175}{163}e^{10} + \frac{47}{163}e^{9} + \frac{2583}{163}e^{8} - \frac{827}{163}e^{7} - \frac{12589}{163}e^{6} + \frac{3900}{163}e^{5} + \frac{23895}{163}e^{4} - \frac{5984}{163}e^{3} - \frac{15291}{163}e^{2} + \frac{2898}{163}e + \frac{1390}{163}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} - w + 1]$ $1$