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gp:[N,k,chi] = [1584,4,Mod(1,1584)]
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("1584.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1584, 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,-8,0,-10]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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
|
| \(2\) |
\( +1 \) |
| \(3\) |
\( +1 \) |
| \(11\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1584))\):
\( T_{5}^{3} + 8T_{5}^{2} - 56T_{5} - 352 \)
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\( T_{7}^{3} + 10T_{7}^{2} - 268T_{7} + 456 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
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|
| $3$ |
\( T^{3} \)
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| $5$ |
\( T^{3} + 8 T^{2} + \cdots - 352 \)
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|
| $7$ |
\( T^{3} + 10 T^{2} + \cdots + 456 \)
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|
| $11$ |
\( (T + 11)^{3} \)
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|
| $13$ |
\( T^{3} + 66 T^{2} + \cdots - 17176 \)
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|
| $17$ |
\( T^{3} + 38 T^{2} + \cdots - 30552 \)
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|
| $19$ |
\( T^{3} + 10 T^{2} + \cdots - 828648 \)
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| $23$ |
\( T^{3} + 80 T^{2} + \cdots + 73568 \)
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| $29$ |
\( T^{3} - 98 T^{2} + \cdots + 1179784 \)
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| $31$ |
\( T^{3} - 196 T^{2} + \cdots + 694464 \)
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| $37$ |
\( T^{3} + 162 T^{2} + \cdots + 2287832 \)
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| $41$ |
\( T^{3} - 342 T^{2} + \cdots - 630504 \)
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| $43$ |
\( T^{3} - 338 T^{2} + \cdots - 1243832 \)
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| $47$ |
\( T^{3} - 268 T^{2} + \cdots + 97410496 \)
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| $53$ |
\( T^{3} + 100 T^{2} + \cdots + 1245696 \)
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| $59$ |
\( T^{3} - 332 T^{2} + \cdots - 11865024 \)
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| $61$ |
\( T^{3} + 598 T^{2} + \cdots - 239670344 \)
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| $67$ |
\( T^{3} - 584 T^{2} + \cdots + 5410816 \)
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| $71$ |
\( T^{3} - 1004 T^{2} + \cdots + 93867648 \)
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| $73$ |
\( T^{3} + 1062 T^{2} + \cdots - 293674616 \)
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| $79$ |
\( T^{3} - 2422 T^{2} + \cdots - 66208696 \)
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| $83$ |
\( T^{3} - 1220 T^{2} + \cdots + 4895424 \)
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| $89$ |
\( T^{3} - 2272 T^{2} + \cdots + 642138112 \)
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| $97$ |
\( T^{3} + 2282 T^{2} + \cdots + 267653432 \)
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