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gp:[N,k,chi] = [32490,2,Mod(1,32490)]
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("32490.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
Newform invariants
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sage:traces = [1,1,0,1,-1,0,-4,1,0,-1,6,0,0,-4,0,1,-4,0,0,-1,0,6,4,0,1,0,0,
-4,-10,0,2,1,0,-4,4,0,4,0,0,-1,10,0,-12,6,0,4,0,0,9,1,0,0,-6,0,-6,-4,0,
-10,4,0,-10,2,0,1,0,0,8,-4,0,4,0,0,6,4,0,0,-24,0,10,-1,0,10,-14,0,4,-12,
0,6,10,0,0,4,0,0,0,0,6,9,0,1]
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
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( +1 \) |
| \(5\) |
\( +1 \) |
| \(19\) |
\( -1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
