[N,k,chi] = [381,2,Mod(25,381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(381, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("381.25");
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
\( T_{2}^{120} + 3 T_{2}^{119} + 32 T_{2}^{118} + 75 T_{2}^{117} + 525 T_{2}^{116} + 1018 T_{2}^{115} + 6458 T_{2}^{114} + 11527 T_{2}^{113} + 72154 T_{2}^{112} + 126963 T_{2}^{111} + 757046 T_{2}^{110} + 1297295 T_{2}^{109} + \cdots + 531625249 \)
acting on \(S_{2}^{\mathrm{new}}(381, [\chi])\).