gp:[N,k,chi] = [28749,2,Mod(1,28749)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28749, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28749.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage:traces = [1,-1,-1,-1,2,1,-1,3,1,-2,4,1,-2,1,-2,-1,-2,-1,-4,-2,1,-4,0,-3,
-1,2,-1,1,-10,2,0,-5,-4,2,-2,-1,0,4,2,6,-6,-1,-8,-4,2,0,0,1,1,1,2,2,14,
1,8,-3,4,10,8,2,14,0,-1,7,-4,4,-12,2,0,2,8,3,10,0,1,4,-4,-2,-4,-2,1,6,
12,-1,-4,8,10,12,14,-2,2,0,0,0,-8,5,-6,-1,4,1]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
gp:f = lf[1] \\ Warning: the index may be different
sage:f.q_expansion() # note that sage often uses an isomorphic number field
gp:mfcoefs(f, 20)
p |
Sign
|
3 |
+1 |
7 |
+1 |
37 |
+1 |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.