[N,k,chi] = [525,2,Mod(16,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([0, 6, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.16");
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
\( T_{2}^{160} + 2 T_{2}^{159} - 28 T_{2}^{158} - 62 T_{2}^{157} + 307 T_{2}^{156} + 728 T_{2}^{155} - 779 T_{2}^{154} - 1646 T_{2}^{153} - 18834 T_{2}^{152} - 60092 T_{2}^{151} + 267096 T_{2}^{150} + 881546 T_{2}^{149} - 1594605 T_{2}^{148} + \cdots + 390625 \)
acting on \(S_{2}^{\mathrm{new}}(525, [\chi])\).