[N,k,chi] = [325,2,Mod(8,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.8");
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
\( T_{2}^{256} + 2 T_{2}^{255} + 100 T_{2}^{254} + 198 T_{2}^{253} + 5236 T_{2}^{252} + 10168 T_{2}^{251} + 190978 T_{2}^{250} + 361444 T_{2}^{249} + 5449809 T_{2}^{248} + 10010684 T_{2}^{247} + 129515090 T_{2}^{246} + \cdots + 20\!\cdots\!61 \)
acting on \(S_{2}^{\mathrm{new}}(325, [\chi])\).