[N,k,chi] = [6005,2,Mod(1,6005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6005, 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("6005.1");
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
|
\(5\) |
\(1\) |
\(1201\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{113} + 3 T_{2}^{112} - 179 T_{2}^{111} - 538 T_{2}^{110} + 15552 T_{2}^{109} + 46831 T_{2}^{108} - 873916 T_{2}^{107} - 2636588 T_{2}^{106} + 35708941 T_{2}^{105} + 107939281 T_{2}^{104} - 1130959591 T_{2}^{103} + \cdots - 28158256848 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6005))\).