[N,k,chi] = [946,2,Mod(49,946)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(946, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([12, 20]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("946.49");
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
\( T_{3}^{176} - 7 T_{3}^{175} - 25 T_{3}^{174} + 268 T_{3}^{173} + 104 T_{3}^{172} - 4299 T_{3}^{171} + 5220 T_{3}^{170} + 20101 T_{3}^{169} - 104534 T_{3}^{168} + 490505 T_{3}^{167} + 770506 T_{3}^{166} - 12277734 T_{3}^{165} + \cdots + 48\!\cdots\!41 \)
acting on \(S_{2}^{\mathrm{new}}(946, [\chi])\).