[N,k,chi] = [891,2,Mod(100,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([16, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.100");
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
\( T_{2}^{102} + 48 T_{2}^{97} + 849 T_{2}^{96} - 78 T_{2}^{95} - 42 T_{2}^{94} - 506 T_{2}^{93} + 543 T_{2}^{92} + 37908 T_{2}^{91} + 482382 T_{2}^{90} + 55125 T_{2}^{89} + 64287 T_{2}^{88} - 320637 T_{2}^{87} - 155952 T_{2}^{86} + \cdots + 331776 \)
acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\).