[N,k,chi] = [786,2,Mod(17,786)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(786, base_ring=CyclotomicField(130))
chi = DirichletCharacter(H, H._module([65, 43]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("786.17");
S:= CuspForms(chi, 2);
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
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
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.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{1056} + 63 T_{5}^{1054} - 75 T_{5}^{1053} + 1696 T_{5}^{1052} - 3711 T_{5}^{1051} + 30367 T_{5}^{1050} - 73873 T_{5}^{1049} + 482702 T_{5}^{1048} - 957509 T_{5}^{1047} + 4965134 T_{5}^{1046} - 12955898 T_{5}^{1045} + \cdots + 12\!\cdots\!76 \)
acting on \(S_{2}^{\mathrm{new}}(786, [\chi])\).