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gp:[N,k,chi] = [15730,2,Mod(1,15730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
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magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
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sage:traces = [1,-1,0,1,1,0,0,-1,-3,-1,0,0,-1,0,0,1,-2,3,8,1,0,0,-4,0,1,1,0,
0,2,0,-4,-1,0,2,0,-3,6,-8,0,-1,-10,0,0,0,-3,4,8,0,-7,-1,0,-1,6,0,0,0,0,
-2,8,0,2,4,0,1,-1,0,4,-2,0,0,-12,3,-10,-6,0,8,0,0,8,1,9,10,-12,0,-2,0,
0,0,10,3,0,-4,0,-8,8,0,-14,7,0,1]
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
|
| \(2\) |
\( +1 \) |
| \(5\) |
\( -1 \) |
| \(11\) |
\( -1 \) |
| \(13\) |
\( +1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
