[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
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.
\( p \) |
Sign
|
\(4021\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{182} - 18 T_{2}^{181} - 124 T_{2}^{180} + 4134 T_{2}^{179} - 1044 T_{2}^{178} - 455572 T_{2}^{177} + 1440385 T_{2}^{176} + 31854125 T_{2}^{175} - 167292476 T_{2}^{174} - 1567946638 T_{2}^{173} + \cdots - 450537346108 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4021))\).