# Properties

 Label 6.6.1683101.1-13.2-e Base field 6.6.1683101.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $13$ Level $[13,13,w^{2} - 2w - 2]$ Dimension $9$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.1683101.1

Generator $$w$$, with minimal polynomial $$x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[13,13,w^{2} - 2w - 2]$ Dimension: $9$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{9} - 4x^{8} - 37x^{7} + 111x^{6} + 584x^{5} - 939x^{4} - 4600x^{3} + 1184x^{2} + 14528x + 10992$$
Norm Prime Eigenvalue
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ $\phantom{-}\frac{105}{3184}e^{8} - \frac{28}{199}e^{7} - \frac{2545}{3184}e^{6} + \frac{8619}{3184}e^{5} + \frac{1470}{199}e^{4} - \frac{41983}{3184}e^{3} - \frac{22723}{796}e^{2} + \frac{3137}{796}e + \frac{3299}{199}$
13 $[13, 13, w^{2} - 3]$ $-\frac{49}{398}e^{8} + \frac{1221}{1592}e^{7} + \frac{1055}{398}e^{6} - \frac{30377}{1592}e^{5} - \frac{37337}{1592}e^{4} + \frac{63717}{398}e^{3} + \frac{231501}{1592}e^{2} - \frac{184571}{398}e - \frac{203905}{398}$
13 $[13, 13, -w^{2} + 2w + 2]$ $-1$
29 $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ $-\frac{167}{1592}e^{8} + \frac{271}{398}e^{7} + \frac{3555}{1592}e^{6} - \frac{27445}{1592}e^{5} - \frac{7959}{398}e^{4} + \frac{235669}{1592}e^{3} + \frac{53171}{398}e^{2} - \frac{175701}{398}e - \frac{99790}{199}$
29 $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ $\phantom{-}\frac{16}{199}e^{8} - \frac{419}{796}e^{7} - \frac{312}{199}e^{6} + \frac{10183}{796}e^{5} + \frac{9759}{796}e^{4} - \frac{20968}{199}e^{3} - \frac{62779}{796}e^{2} + \frac{60727}{199}e + \frac{63515}{199}$
41 $[41, 41, -w^{2} + 4]$ $-\frac{47}{1592}e^{8} + \frac{143}{398}e^{7} + \frac{419}{1592}e^{6} - \frac{16685}{1592}e^{5} - \frac{45}{398}e^{4} + \frac{173133}{1592}e^{3} + \frac{18389}{398}e^{2} - \frac{158527}{398}e - \frac{81276}{199}$
41 $[41, 41, -w^{2} + 2w + 3]$ $-\frac{169}{1592}e^{8} + \frac{867}{1592}e^{7} + \frac{3793}{1592}e^{6} - \frac{9401}{796}e^{5} - \frac{32483}{1592}e^{4} + \frac{122671}{1592}e^{3} + \frac{140139}{1592}e^{2} - \frac{55705}{398}e - \frac{57607}{398}$
43 $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $-\frac{39}{398}e^{8} + \frac{1183}{1592}e^{7} + \frac{661}{398}e^{6} - \frac{30107}{1592}e^{5} - \frac{16835}{1592}e^{4} + \frac{66333}{398}e^{3} + \frac{141743}{1592}e^{2} - \frac{207635}{398}e - \frac{198461}{398}$
43 $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $-\frac{42}{199}e^{8} + \frac{1553}{1592}e^{7} + \frac{2235}{398}e^{6} - \frac{36297}{1592}e^{5} - \frac{94169}{1592}e^{4} + \frac{66501}{398}e^{3} + \frac{479785}{1592}e^{2} - \frac{74709}{199}e - \frac{234501}{398}$
64 $[64, 2, -2]$ $-\frac{281}{3184}e^{8} + \frac{825}{1592}e^{7} + \frac{5977}{3184}e^{6} - \frac{38861}{3184}e^{5} - \frac{24905}{1592}e^{4} + \frac{298103}{3184}e^{3} + \frac{135175}{1592}e^{2} - \frac{190285}{796}e - \frac{105299}{398}$
71 $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ $-\frac{107}{796}e^{8} + \frac{207}{199}e^{7} + \frac{1987}{796}e^{6} - \frac{22065}{796}e^{5} - \frac{4002}{199}e^{4} + \frac{204401}{796}e^{3} + \frac{35780}{199}e^{2} - \frac{167114}{199}e - \frac{181066}{199}$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ $-\frac{247}{1592}e^{8} + \frac{779}{796}e^{7} + \frac{5115}{1592}e^{6} - \frac{37935}{1592}e^{5} - \frac{21495}{796}e^{4} + \frac{308669}{1592}e^{3} + \frac{129435}{796}e^{2} - \frac{214347}{398}e - \frac{112199}{199}$
71 $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $\phantom{-}\frac{15}{199}e^{8} - \frac{57}{796}e^{7} - \frac{591}{199}e^{6} + \frac{405}{796}e^{5} + \frac{30753}{796}e^{4} + \frac{3725}{199}e^{3} - \frac{132249}{796}e^{2} - \frac{33004}{199}e + \frac{5579}{199}$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ $\phantom{-}\frac{81}{398}e^{8} - \frac{2059}{1592}e^{7} - \frac{1679}{398}e^{6} + \frac{50743}{1592}e^{5} + \frac{56855}{1592}e^{4} - \frac{105653}{398}e^{3} - \frac{358651}{1592}e^{2} + \frac{306423}{398}e + \frac{334517}{398}$
83 $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ $-\frac{55}{796}e^{8} + \frac{5}{1592}e^{7} + \frac{2167}{796}e^{6} + \frac{3337}{1592}e^{5} - \frac{53097}{1592}e^{4} - \frac{41651}{796}e^{3} + \frac{172309}{1592}e^{2} + \frac{121733}{398}e + \frac{82539}{398}$
83 $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ $-\frac{21}{199}e^{8} + \frac{219}{398}e^{7} + \frac{509}{199}e^{6} - \frac{5159}{398}e^{5} - \frac{10005}{398}e^{4} + \frac{19660}{199}e^{3} + \frac{54227}{398}e^{2} - \frac{49593}{199}e - \frac{67630}{199}$
97 $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ $-\frac{19}{796}e^{8} + \frac{213}{398}e^{7} - \frac{525}{796}e^{6} - \frac{11919}{796}e^{5} + \frac{6031}{398}e^{4} + \frac{121713}{796}e^{3} - \frac{4249}{398}e^{2} - \frac{112146}{199}e - \frac{95300}{199}$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ $\phantom{-}\frac{101}{1592}e^{8} - \frac{160}{199}e^{7} - \frac{477}{1592}e^{6} + \frac{35855}{1592}e^{5} - \frac{953}{199}e^{4} - \frac{358723}{1592}e^{3} - \frac{26459}{398}e^{2} + \frac{319147}{398}e + \frac{153546}{199}$
113 $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ $-\frac{67}{398}e^{8} + \frac{591}{398}e^{7} + \frac{504}{199}e^{6} - \frac{15825}{398}e^{5} - \frac{6053}{398}e^{4} + \frac{74299}{199}e^{3} + \frac{39815}{199}e^{2} - \frac{247424}{199}e - \frac{252540}{199}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,w^{2} - 2w - 2]$ $1$