[N,k,chi] = [8045,2,Mod(1,8045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8045, 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("8045.1");
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
|
\(5\) |
\(-1\) |
\(1609\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{142} - 21 T_{2}^{141} + 3039 T_{2}^{139} - 15763 T_{2}^{138} - 192561 T_{2}^{137} + 1760982 T_{2}^{136} + 6231649 T_{2}^{135} - 105899723 T_{2}^{134} - 40642006 T_{2}^{133} + 4306862922 T_{2}^{132} + \cdots + 124007569699 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8045))\).