[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, 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("4006.1");
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
|
\(2\) |
\(1\) |
\(2003\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{42} - 91 T_{3}^{40} + T_{3}^{39} + 3807 T_{3}^{38} - 79 T_{3}^{37} - 97088 T_{3}^{36} + 2841 T_{3}^{35} + 1687568 T_{3}^{34} - 61674 T_{3}^{33} - 21178181 T_{3}^{32} + 904084 T_{3}^{31} + 198326153 T_{3}^{30} + \cdots + 2149888 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4006))\).