[N,k,chi] = [8019,2,Mod(1,8019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8019.1");
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
|
\(3\) |
\(-1\) |
\(11\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{21} + 6 T_{2}^{20} - 12 T_{2}^{19} - 130 T_{2}^{18} - 24 T_{2}^{17} + 1146 T_{2}^{16} + 1083 T_{2}^{15} - 5307 T_{2}^{14} - 7305 T_{2}^{13} + 13936 T_{2}^{12} + 24021 T_{2}^{11} - 20871 T_{2}^{10} - 44302 T_{2}^{9} + 16746 T_{2}^{8} + \cdots + 53 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\).