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gp:[N,k,chi] = [8624,2,Mod(1,8624)]
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("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
Newform invariants
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sage:traces = [3,0,5,0,-2,0,0,0,4,0,-3,0,-3,0,-1,0,-11,0,-7,0,0,0,6,0,19,0,
8,0,-3,0,-19,0,-5,0,0,0,12]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(37)] == 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
|
| \(2\) |
\( +1 \) |
| \(7\) |
\( +1 \) |
| \(11\) |
\( +1 \) |
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8624))\):
\( T_{3}^{3} - 5T_{3}^{2} + 6T_{3} - 1 \)
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\( T_{5}^{3} + 2T_{5}^{2} - 15T_{5} - 29 \)
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\( T_{13}^{3} + 3T_{13}^{2} - 4T_{13} + 1 \)
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\( T_{17}^{3} + 11T_{17}^{2} + 24T_{17} - 29 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
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| $3$ |
\( T^{3} - 5 T^{2} + \cdots - 1 \)
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| $5$ |
\( T^{3} + 2 T^{2} + \cdots - 29 \)
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|
| $7$ |
\( T^{3} \)
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|
| $11$ |
\( (T + 1)^{3} \)
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| $13$ |
\( T^{3} + 3 T^{2} + \cdots + 1 \)
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| $17$ |
\( T^{3} + 11 T^{2} + \cdots - 29 \)
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| $19$ |
\( T^{3} + 7 T^{2} + \cdots + 7 \)
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| $23$ |
\( T^{3} - 6 T^{2} + \cdots - 1 \)
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| $29$ |
\( T^{3} + 3 T^{2} + \cdots + 1 \)
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| $31$ |
\( T^{3} + 19 T^{2} + \cdots + 239 \)
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| $37$ |
\( T^{3} - 12 T^{2} + \cdots - 8 \)
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| $41$ |
\( T^{3} + 17 T^{2} + \cdots - 167 \)
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| $43$ |
\( T^{3} + 12 T^{2} + \cdots - 83 \)
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| $47$ |
\( T^{3} - 17 T^{2} + \cdots + 923 \)
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| $53$ |
\( T^{3} + 3 T^{2} + \cdots - 97 \)
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| $59$ |
\( T^{3} - 12 T^{2} + \cdots + 1021 \)
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| $61$ |
\( T^{3} - 84T + 56 \)
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| $67$ |
\( T^{3} - 84T + 56 \)
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| $71$ |
\( T^{3} - 3 T^{2} + \cdots + 41 \)
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| $73$ |
\( T^{3} + 26 T^{2} + \cdots + 113 \)
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| $79$ |
\( T^{3} + 23 T^{2} + \cdots + 433 \)
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| $83$ |
\( T^{3} - 9 T^{2} + \cdots + 673 \)
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| $89$ |
\( T^{3} - 13 T^{2} + \cdots - 29 \)
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| $97$ |
\( T^{3} - T^{2} + \cdots + 911 \)
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