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gp:[N,k,chi] = [1638,4,Mod(1,1638)]
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("1638.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
Newform invariants
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sage:traces = [3,6,0,12,-13,0,21,24,0,-26,-17]
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
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( -1 \) |
| \(7\) |
\( -1 \) |
| \(13\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1638))\):
\( T_{5}^{3} + 13T_{5}^{2} - 146T_{5} + 288 \)
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\( T_{11}^{3} + 17T_{11}^{2} - 2310T_{11} + 10536 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T - 2)^{3} \)
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|
| $3$ |
\( T^{3} \)
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|
| $5$ |
\( T^{3} + 13 T^{2} + \cdots + 288 \)
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|
| $7$ |
\( (T - 7)^{3} \)
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|
| $11$ |
\( T^{3} + 17 T^{2} + \cdots + 10536 \)
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|
| $13$ |
\( (T + 13)^{3} \)
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|
| $17$ |
\( T^{3} + 89 T^{2} + \cdots - 16628 \)
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|
| $19$ |
\( T^{3} - 89 T^{2} + \cdots + 718176 \)
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| $23$ |
\( T^{3} + 289 T^{2} + \cdots - 563424 \)
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| $29$ |
\( T^{3} + 125 T^{2} + \cdots - 2752572 \)
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| $31$ |
\( T^{3} + 208 T^{2} + \cdots - 239488 \)
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| $37$ |
\( T^{3} - 213 T^{2} + \cdots + 5144564 \)
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| $41$ |
\( T^{3} + 530 T^{2} + \cdots - 18905088 \)
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| $43$ |
\( T^{3} + 75 T^{2} + \cdots + 1482192 \)
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| $47$ |
\( T^{3} + 298 T^{2} + \cdots - 62195328 \)
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| $53$ |
\( T^{3} + 710 T^{2} + \cdots + 1248616 \)
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| $59$ |
\( T^{3} - 250 T^{2} + \cdots + 14803488 \)
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| $61$ |
\( T^{3} + 511 T^{2} + \cdots - 63342772 \)
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| $67$ |
\( T^{3} + 522 T^{2} + \cdots - 7056512 \)
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| $71$ |
\( T^{3} + 282 T^{2} + \cdots + 150609024 \)
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| $73$ |
\( T^{3} + 701 T^{2} + \cdots - 298076364 \)
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| $79$ |
\( T^{3} - 1262 T^{2} + \cdots + 144063488 \)
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| $83$ |
\( T^{3} + 1700 T^{2} + \cdots + 161161584 \)
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| $89$ |
\( T^{3} + 1628 T^{2} + \cdots + 32164336 \)
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| $97$ |
\( T^{3} - 1526 T^{2} + \cdots + 199579224 \)
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