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gp:[N,k,chi] = [2142,4,Mod(1,2142)]
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("2142.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2142, 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,-6,0,12,15,0,-21,-24,0,-30,108]
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
|
| \(2\) |
\( +1 \) |
| \(3\) |
\( -1 \) |
| \(7\) |
\( +1 \) |
| \(17\) |
\( -1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2142))\):
\( T_{5}^{3} - 15T_{5}^{2} - 107T_{5} + 518 \)
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\( T_{11}^{3} - 108T_{11}^{2} + 3400T_{11} - 24984 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T + 2)^{3} \)
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|
| $3$ |
\( T^{3} \)
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|
| $5$ |
\( T^{3} - 15 T^{2} + \cdots + 518 \)
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|
| $7$ |
\( (T + 7)^{3} \)
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|
| $11$ |
\( T^{3} - 108 T^{2} + \cdots - 24984 \)
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|
| $13$ |
\( T^{3} - 4 T^{2} + \cdots + 118848 \)
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|
| $17$ |
\( (T - 17)^{3} \)
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|
| $19$ |
\( T^{3} + 32 T^{2} + \cdots - 1001448 \)
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| $23$ |
\( T^{3} - 280 T^{2} + \cdots + 732256 \)
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| $29$ |
\( T^{3} - 502 T^{2} + \cdots - 335328 \)
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| $31$ |
\( T^{3} + 5 T^{2} + \cdots - 3642856 \)
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| $37$ |
\( T^{3} + 118 T^{2} + \cdots - 10746224 \)
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| $41$ |
\( T^{3} + 257 T^{2} + \cdots - 25764042 \)
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| $43$ |
\( T^{3} + 193 T^{2} + \cdots + 103764 \)
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| $47$ |
\( T^{3} + 304 T^{2} + \cdots - 70336896 \)
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| $53$ |
\( T^{3} - 721 T^{2} + \cdots + 88335518 \)
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| $59$ |
\( T^{3} + 418 T^{2} + \cdots - 131279904 \)
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| $61$ |
\( T^{3} + 185 T^{2} + \cdots + 53552406 \)
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| $67$ |
\( T^{3} - 327 T^{2} + \cdots - 24541488 \)
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| $71$ |
\( T^{3} - 818 T^{2} + \cdots + 611148048 \)
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| $73$ |
\( T^{3} - 531 T^{2} + \cdots + 27702 \)
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| $79$ |
\( T^{3} - 808 T^{2} + \cdots + 351828032 \)
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| $83$ |
\( T^{3} + 536 T^{2} + \cdots - 243995864 \)
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| $89$ |
\( T^{3} + 1254 T^{2} + \cdots - 611140576 \)
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| $97$ |
\( T^{3} + \cdots + 1011312386 \)
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