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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,-9,0,0,0,18]
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2160))\):
\( T_{7}^{3} + 9T_{7}^{2} - 588T_{7} - 5524 \)
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\( T_{11}^{3} - 18T_{11}^{2} - 3081T_{11} + 76426 \)
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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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|
| $7$ |
\( T^{3} + 9 T^{2} + \cdots - 5524 \)
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|
| $11$ |
\( T^{3} - 18 T^{2} + \cdots + 76426 \)
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|
| $13$ |
\( T^{3} + 21 T^{2} + \cdots - 30901 \)
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|
| $17$ |
\( T^{3} + 84 T^{2} + \cdots - 86732 \)
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| $19$ |
\( T^{3} + 21 T^{2} + \cdots - 138464 \)
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| $23$ |
\( T^{3} - 48 T^{2} + \cdots + 2038 \)
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| $29$ |
\( T^{3} - 36 T^{2} + \cdots + 3034586 \)
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| $31$ |
\( T^{3} + 324 T^{2} + \cdots - 9213176 \)
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| $37$ |
\( T^{3} - 33 T^{2} + \cdots + 2851956 \)
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| $41$ |
\( T^{3} + 114 T^{2} + \cdots - 1847232 \)
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| $43$ |
\( T^{3} + 282 T^{2} + \cdots - 1113236 \)
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| $47$ |
\( T^{3} - 282 T^{2} + \cdots - 11238296 \)
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| $53$ |
\( T^{3} + 222 T^{2} + \cdots + 5908896 \)
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| $59$ |
\( (T + 92)^{3} \)
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| $61$ |
\( T^{3} - 303 T^{2} + \cdots + 13330220 \)
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| $67$ |
\( T^{3} + 1035 T^{2} + \cdots - 849676336 \)
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| $71$ |
\( T^{3} - 510 T^{2} + \cdots + 11439360 \)
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| $73$ |
\( T^{3} - 447 T^{2} + \cdots + 78574428 \)
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| $79$ |
\( T^{3} + 777 T^{2} + \cdots + 14000175 \)
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| $83$ |
\( T^{3} - 78 T^{2} + \cdots - 87546568 \)
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| $89$ |
\( T^{3} - 324 T^{2} + \cdots - 92454912 \)
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| $97$ |
\( T^{3} - 1191 T^{2} + \cdots + 31736348 \)
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