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gp:[N,k,chi] = [16170,2,Mod(1,16170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16170.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
Newform invariants
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sage:traces = [1,1,-1,1,-1,-1,0,1,1,-1,-1,-1,4,0,1,1,-7,1,-1,-1,0,-1,1,-1,1,
4,-1,0,3,1,-6,1,1,-7,0,1,-3,-1,-4,-1,2,0,7,-1,-1,1,3,-1,0,1,7,4,10,-1,
1,0,1,3,-1,1,4,-6,0,1,-4,1,-10,-7,-1,0,-3,1,-8,-3,-1,-1,0,-4,4,-1,1,2,
10,0,7,7,-3,-1,2,-1,0,1,6,3,1,-1,-17,0,-1,1]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
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gp:f = lf[1] \\ Warning: the index may be different
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sage:f.q_expansion() # note that sage often uses an isomorphic number field
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gp:mfcoefs(f, 20)
| \( p \) |
Sign
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( +1 \) |
| \(5\) |
\( +1 \) |
| \(7\) |
\( -1 \) |
| \(11\) |
\( +1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
