[N,k,chi] = [605,2,Mod(16,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(110))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.16");
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
\( T_{2}^{880} - 2 T_{2}^{879} - 32 T_{2}^{878} + 72 T_{2}^{877} + 423 T_{2}^{876} - 1164 T_{2}^{875} - 2711 T_{2}^{874} + 9338 T_{2}^{873} + 7446 T_{2}^{872} - 7598 T_{2}^{871} - 20117 T_{2}^{870} - 692064 T_{2}^{869} + \cdots + 61\!\cdots\!61 \)
acting on \(S_{2}^{\mathrm{new}}(605, [\chi])\).