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gp:[N,k,chi] = [37479,2,Mod(1,37479)]
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("37479.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37479, 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 = [1,1,1,-1,2,1,-4,-3,1,2,-4,-1,-1,-4,2,-1,-2,1,0,-2,-4,-4,0,-3,
-1,-1,1,4,10,2,0,5,-4,-2,-8,-1,2,0,-1,-6,6,-4,12,4,2,0,0,-1,9,-1,-2,1,
-6,1,-8,12,0,10,12,-2,2,0,-4,7,-2,-4,-8,2,0,-8,0,-3,-2,2,-1,0,16,-1,-8,
-2,1,6,-4,4,-4,12,10,12,2,2,4,0,0,0,0,5,10,9,-4,1]
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
|
| \(3\) |
\( -1 \) |
| \(13\) |
\( +1 \) |
| \(31\) |
\( -1 \) |
Inner twists of this newform have not been computed.
Twists of this newform have not been computed.
