[N,k,chi] = [650,2,Mod(61,650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(650, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([24, 20]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("650.61");
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
\( T_{3}^{136} - 30 T_{3}^{134} - 2 T_{3}^{133} + 308 T_{3}^{132} + 148 T_{3}^{131} + 1527 T_{3}^{130} - 3375 T_{3}^{129} - 74534 T_{3}^{128} + 34148 T_{3}^{127} + 834026 T_{3}^{126} + 19162 T_{3}^{125} - 2388757 T_{3}^{124} + \cdots + 15\!\cdots\!25 \)
acting on \(S_{2}^{\mathrm{new}}(650, [\chi])\).