[N,k,chi] = [375,3,Mod(7,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 17]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.7");
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
\( T_{2}^{80} + 4 T_{2}^{79} + 8 T_{2}^{78} - 24 T_{2}^{77} - 428 T_{2}^{76} - 740 T_{2}^{75} + 102 T_{2}^{74} + 15444 T_{2}^{73} + 98743 T_{2}^{72} + 78556 T_{2}^{71} - 138920 T_{2}^{70} - 3581004 T_{2}^{69} + \cdots + 87\!\cdots\!41 \)
acting on \(S_{3}^{\mathrm{new}}(375, [\chi])\).