[N,k,chi] = [960,2,Mod(61,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.61");
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
\( T_{7}^{240} - 800 T_{7}^{235} + 4864 T_{7}^{234} + 12416 T_{7}^{233} + 1081920 T_{7}^{232} + 188672 T_{7}^{231} + 1602944 T_{7}^{230} - 25090560 T_{7}^{229} + 1896448 T_{7}^{228} - 268509888 T_{7}^{227} + \cdots + 28\!\cdots\!76 \)
acting on \(S_{2}^{\mathrm{new}}(960, [\chi])\).