[N,k,chi] = [945,2,Mod(41,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([17, 0, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.41");
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
\( T_{13}^{288} + 3 T_{13}^{287} + 81 T_{13}^{286} - 228 T_{13}^{285} + 2016 T_{13}^{284} - 14346 T_{13}^{283} - 183213 T_{13}^{282} - 734274 T_{13}^{281} - 21134637 T_{13}^{280} + 82135332 T_{13}^{279} - 675305091 T_{13}^{278} + \cdots + 59\!\cdots\!24 \)
acting on \(S_{2}^{\mathrm{new}}(945, [\chi])\).