Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 51x^{10} + 909x^{8} + 6788x^{6} + 21556x^{4} + 25776x^{2} + 5184\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $-\frac{341}{3191616}e^{11} - \frac{5407}{1063872}e^{9} - \frac{29167}{354624}e^{7} - \frac{860867}{1595808}e^{5} - \frac{320459}{199476}e^{3} - \frac{8761}{3694}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $-\frac{341}{3191616}e^{11} - \frac{5407}{1063872}e^{9} - \frac{29167}{354624}e^{7} - \frac{860867}{1595808}e^{5} - \frac{320459}{199476}e^{3} - \frac{8761}{3694}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, 10w + 4]$ | $-\frac{3965}{2393712}e^{11} - \frac{31427}{398952}e^{9} - \frac{20458}{16623}e^{7} - \frac{16416577}{2393712}e^{5} - \frac{11935933}{1196856}e^{3} + \frac{169835}{33246}e$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}\frac{389}{149607}e^{11} + \frac{50921}{398952}e^{9} + \frac{281699}{132984}e^{7} + \frac{16320065}{1196856}e^{5} + \frac{18975437}{598428}e^{3} + \frac{315530}{16623}e$ |
| 17 | $[17, 17, w + 1]$ | $-\frac{3959}{1595808}e^{10} - \frac{65245}{531936}e^{8} - \frac{361117}{177312}e^{6} - \frac{10141469}{797904}e^{4} - \frac{1204675}{49869}e^{2} - \frac{6505}{5541}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $-\frac{3395}{2393712}e^{11} - \frac{57277}{797904}e^{9} - \frac{334585}{265968}e^{7} - \frac{10786097}{1196856}e^{5} - \frac{15255473}{598428}e^{3} - \frac{666403}{33246}e$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{515}{531936}e^{11} - \frac{8101}{177312}e^{9} - \frac{41125}{59104}e^{7} - \frac{942815}{265968}e^{5} - \frac{99845}{33246}e^{3} + \frac{17755}{3694}e$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $\phantom{-}\frac{8953}{4787424}e^{11} + \frac{141929}{1595808}e^{9} + \frac{742157}{531936}e^{7} + \frac{9499589}{1196856}e^{5} + \frac{15781441}{1196856}e^{3} - \frac{12137}{33246}e$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $-\frac{605}{99738}e^{10} - \frac{38551}{132984}e^{8} - \frac{203953}{44328}e^{6} - \frac{10759687}{398952}e^{4} - \frac{9739129}{199476}e^{2} - \frac{47515}{5541}$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $-\frac{301}{398952}e^{11} - \frac{1181}{33246}e^{9} - \frac{2944}{5541}e^{7} - \frac{983789}{398952}e^{5} + \frac{10462}{49869}e^{3} + \frac{35277}{3694}e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{2491}{797904}e^{10} + \frac{40733}{265968}e^{8} + \frac{224309}{88656}e^{6} + \frac{6362035}{398952}e^{4} + \frac{3370727}{99738}e^{2} + \frac{85354}{5541}$ |
| 29 | $[29, 29, w + 7]$ | $-\frac{10111}{4787424}e^{11} - \frac{162533}{1595808}e^{9} - \frac{875621}{531936}e^{7} - \frac{23977165}{2393712}e^{5} - \frac{2878298}{149607}e^{3} - \frac{25964}{16623}e$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $\phantom{-}\frac{19129}{4787424}e^{11} + \frac{309035}{1595808}e^{9} + \frac{1671923}{531936}e^{7} + \frac{46290667}{2393712}e^{5} + \frac{24618155}{598428}e^{3} + \frac{753415}{33246}e$ |
| 43 | $[43, 43, w^{2} - 11]$ | $\phantom{-}\frac{3295}{797904}e^{10} + \frac{52799}{265968}e^{8} + \frac{284531}{88656}e^{6} + \frac{3965621}{199476}e^{4} + \frac{8540989}{199476}e^{2} + \frac{100780}{5541}$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $\phantom{-}\frac{65}{88656}e^{10} + \frac{879}{29552}e^{8} + \frac{10981}{29552}e^{6} + \frac{61757}{44328}e^{4} + \frac{8473}{11082}e^{2} + \frac{2046}{1847}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{1355}{398952}e^{10} - \frac{5611}{33246}e^{8} - \frac{62897}{22164}e^{6} - \frac{7375429}{398952}e^{4} - \frac{8388475}{199476}e^{2} - \frac{83560}{5541}$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}\frac{2053}{531936}e^{10} + \frac{32423}{177312}e^{8} + \frac{169751}{59104}e^{6} + \frac{4468231}{265968}e^{4} + \frac{1094575}{33246}e^{2} + \frac{20460}{1847}$ |
| 79 | $[79, 79, w^{2} + 37]$ | $-\frac{5323}{1595808}e^{11} - \frac{86873}{531936}e^{9} - \frac{477785}{177312}e^{7} - \frac{13584937}{797904}e^{5} - \frac{1845593}{49869}e^{3} - \frac{111637}{5541}e$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $-\frac{7925}{1595808}e^{10} - \frac{130471}{531936}e^{8} - \frac{716983}{177312}e^{6} - \frac{19851935}{797904}e^{4} - \frac{4854917}{99738}e^{2} - \frac{104800}{5541}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2}]$ | $\frac{341}{3191616}e^{11} + \frac{5407}{1063872}e^{9} + \frac{29167}{354624}e^{7} + \frac{860867}{1595808}e^{5} + \frac{320459}{199476}e^{3} + \frac{8761}{3694}e$ |
| $4$ | $[4, 2, w^{2} + w + 1]$ | $\frac{341}{3191616}e^{11} + \frac{5407}{1063872}e^{9} + \frac{29167}{354624}e^{7} + \frac{860867}{1595808}e^{5} + \frac{320459}{199476}e^{3} + \frac{8761}{3694}e$ |