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gp:[N,k,chi] = [30345,2,Mod(1,30345)]
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("30345.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30345, 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,-1,1,1,1,3,1,-1,-2,1,2,-1,-1,-1,0,-1,-2,-1,-1,2,2,-3,
1,-2,-1,-1,10,1,8,-5,2,0,1,-1,8,2,-2,3,-2,1,-12,2,1,-2,-12,1,1,-1,0,-2,
6,1,-2,3,2,-10,0,1,-6,-8,1,7,2,-2,-4,0,-2,-1,-6,3,10,-8,-1,2,-2,2,-8,-1,
1,2,-16,1,0,12,-10,-6,8,-1,2,-2,-8,12,-2,5,-2,-1,-2,-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
|
| \(3\) |
\( +1 \) |
| \(5\) |
\( -1 \) |
| \(7\) |
\( -1 \) |
| \(17\) |
\( +1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
