[N,k,chi] = [225,3,Mod(28,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.28");
S:= CuspForms(chi, 3);
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
\( T_{2}^{80} + 4 T_{2}^{79} + 8 T_{2}^{78} - 4 T_{2}^{77} - 348 T_{2}^{76} - 580 T_{2}^{75} + 1122 T_{2}^{74} + 13404 T_{2}^{73} + 98023 T_{2}^{72} + 86076 T_{2}^{71} - 324840 T_{2}^{70} - 2770704 T_{2}^{69} + \cdots + 87\!\cdots\!41 \)
acting on \(S_{3}^{\mathrm{new}}(225, [\chi])\).