[N,k,chi] = [567,4,Mod(1,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(3\)
\(-1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{9} - 6T_{2}^{8} - 36T_{2}^{7} + 231T_{2}^{6} + 342T_{2}^{5} - 2619T_{2}^{4} - 603T_{2}^{3} + 9234T_{2}^{2} - 1944T_{2} - 2808 \)
T2^9 - 6*T2^8 - 36*T2^7 + 231*T2^6 + 342*T2^5 - 2619*T2^4 - 603*T2^3 + 9234*T2^2 - 1944*T2 - 2808
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(567))\).
$p$
$F_p(T)$
$2$
\( T^{9} - 6 T^{8} - 36 T^{7} + \cdots - 2808 \)
T^9 - 6*T^8 - 36*T^7 + 231*T^6 + 342*T^5 - 2619*T^4 - 603*T^3 + 9234*T^2 - 1944*T - 2808
$3$
\( T^{9} \)
T^9
$5$
\( T^{9} - 24 T^{8} + \cdots - 705922182 \)
T^9 - 24*T^8 - 414*T^7 + 13326*T^6 - 4977*T^5 - 1591434*T^4 + 4637457*T^3 + 58055292*T^2 - 105967683*T - 705922182
$7$
\( (T - 7)^{9} \)
(T - 7)^9
$11$
\( T^{9} - 111 T^{8} + \cdots + 101515621572 \)
T^9 - 111*T^8 - 360*T^7 + 399558*T^6 - 13529223*T^5 + 67023207*T^4 + 2225301705*T^3 - 27043506855*T^2 + 67898310264*T + 101515621572
$13$
\( T^{9} - 18 T^{8} + \cdots - 3228162266096 \)
T^9 - 18*T^8 - 7659*T^7 + 40422*T^6 + 18508491*T^5 + 183261978*T^4 - 13330412025*T^3 - 326853788670*T^2 - 2321579535336*T - 3228162266096
$17$
\( T^{9} - 273 T^{8} + \cdots - 50\!\cdots\!16 \)
T^9 - 273*T^8 + 9954*T^7 + 2957754*T^6 - 242323227*T^5 - 4683127833*T^4 + 718718485203*T^3 + 950735023749*T^2 - 549339878122704*T - 5020282494076716
$19$
\( T^{9} - 45 T^{8} + \cdots - 278256660857 \)
T^9 - 45*T^8 - 22806*T^7 - 132108*T^6 + 110526219*T^5 + 2455510023*T^4 - 77545772169*T^3 - 1347895653579*T^2 - 4975695962487*T - 278256660857
$23$
\( T^{9} - 312 T^{8} + \cdots + 74\!\cdots\!56 \)
T^9 - 312*T^8 - 35811*T^7 + 15076086*T^6 + 526776309*T^5 - 247538501874*T^4 - 7655010376986*T^3 + 1343590301108142*T^2 + 70483005179535321*T + 744636402132581556
$29$
\( T^{9} - 378 T^{8} + \cdots + 17\!\cdots\!56 \)
T^9 - 378*T^8 - 16227*T^7 + 19161918*T^6 - 1377334854*T^5 - 177359664204*T^4 + 21134168032077*T^3 + 25715303195112*T^2 - 64640541061100052*T + 1788835241582143056
$31$
\( T^{9} - 18 T^{8} + \cdots + 32\!\cdots\!68 \)
T^9 - 18*T^8 - 116091*T^7 + 658668*T^6 + 4448676402*T^5 + 42147947286*T^4 - 60588606938397*T^3 - 1512636645269034*T^2 + 140105079323297172*T + 3299161178497828168
$37$
\( T^{9} + 36 T^{8} + \cdots + 12\!\cdots\!32 \)
T^9 + 36*T^8 - 174303*T^7 - 6232920*T^6 + 8139492702*T^5 + 456605766864*T^4 - 88948378105503*T^3 - 5910471677746638*T^2 + 41731167377448108*T + 1222496532105697432
$41$
\( T^{9} - 477 T^{8} + \cdots - 75\!\cdots\!88 \)
T^9 - 477*T^8 - 265734*T^7 + 128351394*T^6 + 16108026201*T^5 - 9108899696853*T^4 + 19483562156967*T^3 + 119080643611727601*T^2 + 2819673630562803264*T - 75966519630579653088
$43$
\( T^{9} + 171 T^{8} + \cdots + 30\!\cdots\!36 \)
T^9 + 171*T^8 - 259839*T^7 - 49211277*T^6 + 20173162878*T^5 + 4131567863532*T^4 - 413950919269389*T^3 - 87863178745248435*T^2 + 1606059238993524288*T + 305668361492223545836
$47$
\( T^{9} - 654 T^{8} + \cdots + 15\!\cdots\!52 \)
T^9 - 654*T^8 - 255645*T^7 + 244418838*T^6 - 22717005480*T^5 - 15583497218334*T^4 + 3777721345213659*T^3 - 164447764529153616*T^2 - 20782335997955478240*T + 1517885531356221361152
$53$
\( T^{9} - 948 T^{8} + \cdots + 84\!\cdots\!24 \)
T^9 - 948*T^8 + 49698*T^7 + 217318746*T^6 - 102488663079*T^5 + 21981354006150*T^4 - 2602374112241811*T^3 + 173470908732652440*T^2 - 6036406494071921604*T + 84265412689816836624
$59$
\( T^{9} - 957 T^{8} + \cdots + 73\!\cdots\!36 \)
T^9 - 957*T^8 - 834201*T^7 + 719343597*T^6 + 323529257772*T^5 - 170913913089264*T^4 - 64342147124703465*T^3 + 10234589049715716063*T^2 + 3772761339908088167472*T + 7319657619856151109036
$61$
\( T^{9} + 198 T^{8} + \cdots + 58\!\cdots\!28 \)
T^9 + 198*T^8 - 1115847*T^7 - 411485316*T^6 + 258890302431*T^5 + 150721433605242*T^4 + 17233254652075554*T^3 - 1146064586862349710*T^2 - 159999023350466999559*T + 5827324755479870865628
$67$
\( T^{9} + 333 T^{8} + \cdots + 10\!\cdots\!04 \)
T^9 + 333*T^8 - 863748*T^7 - 230141814*T^6 + 232871871339*T^5 + 45019522272267*T^4 - 23489435923301985*T^3 - 3546120828983127381*T^2 + 754204009393971305208*T + 105173083084939286414104
$71$
\( T^{9} - 2826 T^{8} + \cdots - 32\!\cdots\!96 \)
T^9 - 2826*T^8 + 2041848*T^7 + 1167567156*T^6 - 2270401638417*T^5 + 981095862050982*T^4 - 49418156279877543*T^3 - 52422234683323826538*T^2 + 8277446965097636193861*T - 32905703557199586642696
$73$
\( T^{9} - 153 T^{8} + \cdots + 34\!\cdots\!64 \)
T^9 - 153*T^8 - 1419381*T^7 + 419085309*T^6 + 375381079398*T^5 - 66063856098978*T^4 - 31652703309044445*T^3 - 282861283492595907*T^2 + 528010187321906124120*T + 34045939595237859405964
$79$
\( T^{9} - 1152 T^{8} + \cdots + 10\!\cdots\!14 \)
T^9 - 1152*T^8 - 799974*T^7 + 1217064342*T^6 - 134878075839*T^5 - 217649954864268*T^4 + 66791216740123929*T^3 - 2987525702792345850*T^2 - 9058813637339975967*T + 1042203446835962414014
$83$
\( T^{9} - 1890 T^{8} + \cdots - 67\!\cdots\!88 \)
T^9 - 1890*T^8 - 314982*T^7 + 2297361762*T^6 - 895167883269*T^5 - 497297783515392*T^4 + 304618681163004039*T^3 - 4183615673529821388*T^2 - 10662143964958530814644*T - 676830483600313114713888
$89$
\( T^{9} - 1302 T^{8} + \cdots + 15\!\cdots\!08 \)
T^9 - 1302*T^8 - 3706974*T^7 + 5558213076*T^6 + 3455975380041*T^5 - 7425601308907074*T^4 + 603436160810412567*T^3 + 3034269472546299838590*T^2 - 1366938740026432110089160*T + 154445017566529298316248208
$97$
\( T^{9} + 1737 T^{8} + \cdots - 34\!\cdots\!08 \)
T^9 + 1737*T^8 - 3962997*T^7 - 7358450505*T^6 + 3259877000526*T^5 + 7663506049295442*T^4 + 5321957188441791*T^3 - 2163545221399138144377*T^2 - 598364864818220042409888*T - 34272508211020226912246108
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