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gp:[N,k,chi] = [1911,4,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
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magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1911.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Newform invariants
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sage:traces = [3,0,9,-2,-27]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == 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
|
| \(3\) |
\( -1 \) |
| \(7\) |
\( +1 \) |
| \(13\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1911))\):
\( T_{2}^{3} - 11T_{2} - 7 \)
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\( T_{5}^{3} + 27T_{5}^{2} + 144T_{5} - 351 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} - 11T - 7 \)
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|
| $3$ |
\( (T - 3)^{3} \)
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|
| $5$ |
\( T^{3} + 27 T^{2} + \cdots - 351 \)
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|
| $7$ |
\( T^{3} \)
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|
| $11$ |
\( T^{3} + 19 T^{2} + \cdots + 2067 \)
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|
| $13$ |
\( (T + 13)^{3} \)
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|
| $17$ |
\( T^{3} - 25 T^{2} + \cdots - 9529 \)
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|
| $19$ |
\( T^{3} + 169 T^{2} + \cdots - 56609 \)
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|
| $23$ |
\( T^{3} - 28 T^{2} + \cdots + 106197 \)
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|
| $29$ |
\( T^{3} - 274 T^{2} + \cdots + 1429589 \)
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|
| $31$ |
\( T^{3} - 118 T^{2} + \cdots + 1607109 \)
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|
| $37$ |
\( T^{3} - 151 T^{2} + \cdots + 5997719 \)
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| $41$ |
\( T^{3} + 66 T^{2} + \cdots - 5892039 \)
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| $43$ |
\( T^{3} - 598 T^{2} + \cdots - 349639 \)
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| $47$ |
\( T^{3} + 682 T^{2} + \cdots + 10637368 \)
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| $53$ |
\( T^{3} + 467 T^{2} + \cdots - 4904691 \)
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| $59$ |
\( T^{3} + 289 T^{2} + \cdots - 15063589 \)
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| $61$ |
\( T^{3} + 577 T^{2} + \cdots - 30485213 \)
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| $67$ |
\( T^{3} - 839 T^{2} + \cdots + 5470059 \)
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| $71$ |
\( T^{3} - 1039 T^{2} + \cdots + 183869749 \)
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| $73$ |
\( T^{3} + 434 T^{2} + \cdots + 7125809 \)
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| $79$ |
\( T^{3} + 1260 T^{2} + \cdots + 55941927 \)
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| $83$ |
\( T^{3} - 836 T^{2} + \cdots - 41702703 \)
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| $89$ |
\( T^{3} - 787 T^{2} + \cdots + 363386301 \)
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| $97$ |
\( T^{3} - 267 T^{2} + \cdots + 710857157 \)
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