![Copy content]()
gp:[N,k,chi] = [32634,2,Mod(1,32634)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32634.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32634, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
Newform invariants
![Copy content]()
sage:traces = [1,-1,0,1,4,0,0,-1,0,-4,4,0,-5,0,0,1,-7,0,8,4,0,-4,1,0,11,5,0,
0,4,0,2,-1,0,7,0,0,-1,-8,0,-4,-2,0,-9,4,0,-1,-6,0,0,-11,0,-5,1,0,16,0,
0,-4,-6,0,1,-2,0,1,-20,0,-4,-7,0,0,8,0,1,1,0,8,0,0,0,4,0,2,13,0,-28,9,
0,-4,1,0,0,1,0,6,32,0,8,0,0,11]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
![Copy content]()
gp:f = lf[1] \\ Warning: the index may be different
![Copy content]()
sage:f.q_expansion() # note that sage often uses an isomorphic number field
![Copy content]()
gp:mfcoefs(f, 20)
| \( p \) |
Sign
|
| \(2\) |
\( +1 \) |
| \(3\) |
\( -1 \) |
| \(7\) |
\( +1 \) |
| \(37\) |
\( +1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
