[N,k,chi] = [945,2,Mod(121,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.121");
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
\( T_{2}^{300} + 2321 T_{2}^{294} - 3 T_{2}^{293} - 108 T_{2}^{292} - 456 T_{2}^{291} - 963 T_{2}^{290} - 702 T_{2}^{289} + 3027341 T_{2}^{288} + 13719 T_{2}^{287} - 108759 T_{2}^{286} - 993437 T_{2}^{285} + \cdots + 53\!\cdots\!21 \)
acting on \(S_{2}^{\mathrm{new}}(945, [\chi])\).