[N,k,chi] = [840,2,Mod(43,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("840.43");
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
\( T_{13}^{72} + 224 T_{13}^{69} + 6984 T_{13}^{68} + 7424 T_{13}^{67} + 25088 T_{13}^{66} + 1302784 T_{13}^{65} + 21317904 T_{13}^{64} + 43817984 T_{13}^{63} + 144166912 T_{13}^{62} + 3156340224 T_{13}^{61} + \cdots + 18\!\cdots\!56 \)
acting on \(S_{2}^{\mathrm{new}}(840, [\chi])\).