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gp:[N,k,chi] = [2366,4,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2366.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Newform invariants
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sage:traces = [3,-6,-4,12,27]
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
|
| \(2\) |
\( +1 \) |
| \(7\) |
\( +1 \) |
| \(13\) |
\( -1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2366))\):
\( T_{3}^{3} + 4T_{3}^{2} - 52T_{3} - 214 \)
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\( T_{5}^{3} - 27T_{5}^{2} + 135T_{5} + 577 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T + 2)^{3} \)
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|
| $3$ |
\( T^{3} + 4 T^{2} + \cdots - 214 \)
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|
| $5$ |
\( T^{3} - 27 T^{2} + \cdots + 577 \)
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|
| $7$ |
\( (T + 7)^{3} \)
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|
| $11$ |
\( T^{3} - 32 T^{2} + \cdots - 17682 \)
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|
| $13$ |
\( T^{3} \)
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|
| $17$ |
\( T^{3} + 132 T^{2} + \cdots + 40102 \)
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|
| $19$ |
\( T^{3} - 27 T^{2} + \cdots - 50833 \)
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| $23$ |
\( T^{3} - 15 T^{2} + \cdots - 479241 \)
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| $29$ |
\( T^{3} + 51 T^{2} + \cdots - 250047 \)
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| $31$ |
\( T^{3} + 127 T^{2} + \cdots - 2275917 \)
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| $37$ |
\( T^{3} - 344 T^{2} + \cdots + 6180402 \)
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| $41$ |
\( T^{3} + 574 T^{2} + \cdots - 43093848 \)
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| $43$ |
\( T^{3} + 681 T^{2} + \cdots + 545731 \)
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| $47$ |
\( T^{3} - 29 T^{2} + \cdots - 14344291 \)
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| $53$ |
\( T^{3} - 317 T^{2} + \cdots + 3443153 \)
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| $59$ |
\( T^{3} + 606 T^{2} + \cdots - 220284 \)
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| $61$ |
\( T^{3} + 1394 T^{2} + \cdots + 93701016 \)
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| $67$ |
\( T^{3} + 1100 T^{2} + \cdots - 81648144 \)
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| $71$ |
\( T^{3} - 1230 T^{2} + \cdots - 15788934 \)
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| $73$ |
\( T^{3} - 435 T^{2} + \cdots - 23051117 \)
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| $79$ |
\( T^{3} + 189 T^{2} + \cdots - 235809153 \)
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| $83$ |
\( T^{3} - 751 T^{2} + \cdots - 102286083 \)
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| $89$ |
\( T^{3} + 745 T^{2} + \cdots - 456544113 \)
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| $97$ |
\( T^{3} + 1141 T^{2} + \cdots - 20359717 \)
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