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gp:[N,k,chi] = [13650,2,Mod(1,13650)]
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("13650.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13650, 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,-1,1,1,0,-1,-1,-1,1,0,2,1,-1,1,0,1,0,-1,-7,0,-1,-2,2,-1,0,
1,1,-1,-1,0,6,-1,2,0,0,1,11,7,-1,0,-3,1,0,2,0,-2,7,1,1,0,0,-1,-1,-1,0,
1,-7,1,4,0,4,-6,-1,1,0,-2,1,0,2,0,-13,-1,2,-11,0,-7,-2,1,-11,0,1,3,-8,
-1,0,0,-1,-2,-6,0,1,2,6,-7,0,-1,6,-1,2,0]
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
|
| \(2\) |
\( +1 \) |
| \(3\) |
\( -1 \) |
| \(5\) |
\( +1 \) |
| \(7\) |
\( +1 \) |
| \(13\) |
\( +1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
