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gp:[N,k,chi] = [2160,4,Mod(1,2160)]
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("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
Newform invariants
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sage:traces = [3,0,0,0,-15,0,8,0,0,0,-10]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
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gp:f = lf[1] \\ Warning: the index may be different
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
|
| \(2\) |
\( +1 \) |
| \(3\) |
\( +1 \) |
| \(5\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2160))\):
\( T_{7}^{3} - 8T_{7}^{2} - 756T_{7} - 5832 \)
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\( T_{11}^{3} + 10T_{11}^{2} - 2864T_{11} - 59400 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
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| $3$ |
\( T^{3} \)
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| $5$ |
\( (T + 5)^{3} \)
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|
| $7$ |
\( T^{3} - 8 T^{2} + \cdots - 5832 \)
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|
| $11$ |
\( T^{3} + 10 T^{2} + \cdots - 59400 \)
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|
| $13$ |
\( T^{3} - 48 T^{2} + \cdots + 118584 \)
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| $17$ |
\( T^{3} + 37 T^{2} + \cdots - 15597 \)
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| $19$ |
\( T^{3} + 29 T^{2} + \cdots + 22675 \)
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| $23$ |
\( T^{3} + 11 T^{2} + \cdots - 44775 \)
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| $29$ |
\( T^{3} + 28 T^{2} + \cdots + 296760 \)
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| $31$ |
\( T^{3} + 41 T^{2} + \cdots + 291591 \)
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| $37$ |
\( T^{3} - 230 T^{2} + \cdots + 4001784 \)
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| $41$ |
\( T^{3} + 370 T^{2} + \cdots - 2205432 \)
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| $43$ |
\( T^{3} - 130 T^{2} + \cdots + 16735752 \)
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| $47$ |
\( T^{3} + 56 T^{2} + \cdots - 7432640 \)
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| $53$ |
\( T^{3} + 805 T^{2} + \cdots + 7723035 \)
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| $59$ |
\( T^{3} - 576 T^{2} + \cdots + 227290536 \)
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| $61$ |
\( T^{3} + 257 T^{2} + \cdots + 37318467 \)
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| $67$ |
\( T^{3} - 14 T^{2} + \cdots + 30539000 \)
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| $71$ |
\( T^{3} - 1238 T^{2} + \cdots - 9117432 \)
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| $73$ |
\( T^{3} + 398 T^{2} + \cdots + 1074888 \)
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| $79$ |
\( T^{3} - 321 T^{2} + \cdots - 143418599 \)
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| $83$ |
\( T^{3} - 687 T^{2} + \cdots + 435938355 \)
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| $89$ |
\( T^{3} + 2358 T^{2} + \cdots + 374731256 \)
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| $97$ |
\( T^{3} - 576 T^{2} + \cdots + 257454592 \)
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