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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,-7,0,-21,-24,0,14,47]
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1638))\):
\( T_{5}^{3} + 7T_{5}^{2} - 296T_{5} - 1964 \)
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\( T_{11}^{3} - 47T_{11}^{2} - 984T_{11} + 3448 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T + 2)^{3} \)
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|
| $3$ |
\( T^{3} \)
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| $5$ |
\( T^{3} + 7 T^{2} + \cdots - 1964 \)
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|
| $7$ |
\( (T + 7)^{3} \)
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|
| $11$ |
\( T^{3} - 47 T^{2} + \cdots + 3448 \)
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|
| $13$ |
\( (T - 13)^{3} \)
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|
| $17$ |
\( T^{3} + 119 T^{2} + \cdots - 194036 \)
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| $19$ |
\( T^{3} - 101 T^{2} + \cdots + 627408 \)
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| $23$ |
\( T^{3} - 27 T^{2} + \cdots - 1092176 \)
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| $29$ |
\( T^{3} + 345 T^{2} + \cdots - 766124 \)
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| $31$ |
\( T^{3} - 152 T^{2} + \cdots + 6359808 \)
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| $37$ |
\( T^{3} - 227 T^{2} + \cdots + 14102884 \)
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| $41$ |
\( T^{3} + 452 T^{2} + \cdots - 22130464 \)
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| $43$ |
\( T^{3} + 415 T^{2} + \cdots - 10979984 \)
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| $47$ |
\( T^{3} + 240 T^{2} + \cdots + 2336256 \)
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| $53$ |
\( T^{3} + 874 T^{2} + \cdots - 122678856 \)
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| $59$ |
\( T^{3} + 948 T^{2} + \cdots - 37429152 \)
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| $61$ |
\( T^{3} - 951 T^{2} + \cdots + 19045396 \)
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| $67$ |
\( T^{3} - 742 T^{2} + \cdots + 361415456 \)
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| $71$ |
\( T^{3} + 732 T^{2} + \cdots - 9364832 \)
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| $73$ |
\( T^{3} + 585 T^{2} + \cdots - 521616492 \)
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| $79$ |
\( T^{3} + 618 T^{2} + \cdots - 31490368 \)
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| $83$ |
\( T^{3} + \cdots - 1517033360 \)
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| $89$ |
\( T^{3} + 730 T^{2} + \cdots - 51996408 \)
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| $97$ |
\( T^{3} - 2518 T^{2} + \cdots - 430337608 \)
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