gp:[N,k,chi] = [42978,2,Mod(1,42978)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42978, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("42978.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: |
N |
= |
42978=2⋅3⋅13⋅19⋅29 |
Weight: |
k |
= |
2 |
Character orbit: |
[χ] |
= |
42978.a (trivial) |
Newform invariants
sage:traces = [1,1,1,1,-1,1,-5,1,1,-1,-6,1,1,-5,-1,1,-4,1,-1,-1,-5,-6,-3,1,
-4,1,1,-5,-1,-1,0,1,-6,-4,5,1,-5,-1,1,-1,-8,-5,-10,-6,-1,-3,12,1,18,-4,
-4,1,-11,1,6,-5,-1,-1,-11,-1,-5,0,-5,1,-1,-6,2,-4,-3,5,-9,1,-16,-5,-4,
-1,30,1,-13,-1,1,-8,12,-5,4,-10,-1,-6,6,-1,-5,-3,0,12,1,1,13,18,-6,-4]
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
|
2 |
−1 |
3 |
−1 |
13 |
−1 |
19 |
+1 |
29 |
+1 |
This newform does not admit any (nontrivial) inner twists.
Twists of this newform have not been computed.