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gp:[N,k,chi] = [2116,4,Mod(1,2116)]
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("2116.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2116, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
Newform invariants
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sage:traces = [30,0,-2,0,-50]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
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gp:f = lf[1] \\ Warning: the index may be different
The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
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gp:mfembed(f)
| \( p \) |
Sign
|
| \(2\) |
\( -1 \) |
| \(23\) |
\( +1 \) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2116))\):
\( T_{3}^{30} + 2 T_{3}^{29} - 539 T_{3}^{28} - 974 T_{3}^{27} + 127882 T_{3}^{26} + 206494 T_{3}^{25} + \cdots - 57\!\cdots\!31 \)
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\( T_{5}^{30} + 50 T_{5}^{29} - 1018 T_{5}^{28} - 85216 T_{5}^{27} + 63111 T_{5}^{26} + \cdots + 69\!\cdots\!97 \)
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