[N,k,chi] = [804,2,Mod(43,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.43");
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
\( T_{7}^{340} + 4 T_{7}^{339} + 150 T_{7}^{338} + 620 T_{7}^{337} + 12195 T_{7}^{336} + 51142 T_{7}^{335} + 715510 T_{7}^{334} + 3019788 T_{7}^{333} + 34137113 T_{7}^{332} + 144795186 T_{7}^{331} + \cdots + 36\!\cdots\!01 \)
acting on \(S_{2}^{\mathrm{new}}(804, [\chi])\).