[N,k,chi] = [374,2,Mod(9,374)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(374, base_ring=CyclotomicField(40))
chi = DirichletCharacter(H, H._module([24, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("374.9");
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
\( T_{3}^{160} - 4 T_{3}^{158} - 36 T_{3}^{157} + 8 T_{3}^{156} - 16 T_{3}^{155} + 692 T_{3}^{154} + 1864 T_{3}^{153} - 11606 T_{3}^{152} - 22080 T_{3}^{151} - 1216 T_{3}^{150} + 459300 T_{3}^{149} + 149368 T_{3}^{148} + \cdots + 70\!\cdots\!01 \)
acting on \(S_{2}^{\mathrm{new}}(374, [\chi])\).