[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
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
|
\(2\) |
\(-1\) |
\(5\) |
\(-1\) |
\(401\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{29} + 3 T_{3}^{28} - 44 T_{3}^{27} - 130 T_{3}^{26} + 851 T_{3}^{25} + 2470 T_{3}^{24} - 9512 T_{3}^{23} - 27088 T_{3}^{22} + 67874 T_{3}^{21} + 189949 T_{3}^{20} - 321767 T_{3}^{19} - 891226 T_{3}^{18} + 1019291 T_{3}^{17} + \cdots + 4 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8020))\).