[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
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
|
\(5\) |
\(-1\) |
\(11\) |
\(1\) |
\(73\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{38} - 4 T_{2}^{37} - 55 T_{2}^{36} + 231 T_{2}^{35} + 1363 T_{2}^{34} - 6076 T_{2}^{33} - 20091 T_{2}^{32} + 96455 T_{2}^{31} + 195624 T_{2}^{30} - 1032379 T_{2}^{29} - 1318302 T_{2}^{28} + 7883197 T_{2}^{27} + \cdots + 192 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\).