[N,k,chi] = [966,2,Mod(25,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 44, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.25");
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
\( T_{5}^{160} - 2 T_{5}^{159} - 39 T_{5}^{158} + 2 T_{5}^{157} + 775 T_{5}^{156} + 2105 T_{5}^{155} - 8790 T_{5}^{154} - 69004 T_{5}^{153} + 51413 T_{5}^{152} + 1348378 T_{5}^{151} - 37757 T_{5}^{150} - 15719491 T_{5}^{149} + \cdots + 47\!\cdots\!81 \)
acting on \(S_{2}^{\mathrm{new}}(966, [\chi])\).