[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4016.1");
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
|
\(2\) |
\(1\) |
\(251\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{23} + 2 T_{3}^{22} - 55 T_{3}^{21} - 107 T_{3}^{20} + 1286 T_{3}^{19} + 2405 T_{3}^{18} - 16716 T_{3}^{17} - 29527 T_{3}^{16} + 132795 T_{3}^{15} + 215665 T_{3}^{14} - 668901 T_{3}^{13} - 957238 T_{3}^{12} + \cdots + 1408 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4016))\).