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gp:[N,k,chi] = [9802,2,Mod(1,9802)]
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("9802.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9802, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
Newform invariants
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sage:traces = [3,3,3,3,-2,3,3]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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
|
| \(2\) |
\( -1 \) |
| \(13\) |
\( +1 \) |
| \(29\) |
\( +1 \) |
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9802))\):
\( T_{3}^{3} - 3T_{3}^{2} - 4T_{3} + 13 \)
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\( T_{5}^{3} + 2T_{5}^{2} - 8T_{5} - 8 \)
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|
\( T_{7}^{3} - 3T_{7}^{2} - 4T_{7} - 1 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T - 1)^{3} \)
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|
| $3$ |
\( T^{3} - 3 T^{2} + \cdots + 13 \)
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|
| $5$ |
\( T^{3} + 2 T^{2} + \cdots - 8 \)
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|
| $7$ |
\( T^{3} - 3 T^{2} + \cdots - 1 \)
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|
| $11$ |
\( T^{3} + 7T^{2} - 49 \)
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|
| $13$ |
\( T^{3} \)
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|
| $17$ |
\( T^{3} - 2 T^{2} + \cdots + 8 \)
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|
| $19$ |
\( T^{3} + 3 T^{2} + \cdots - 13 \)
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|
| $23$ |
\( T^{3} + 3 T^{2} + \cdots - 97 \)
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|
| $29$ |
\( (T + 1)^{3} \)
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|
| $31$ |
\( T^{3} - 12 T^{2} + \cdots + 104 \)
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|
| $37$ |
\( T^{3} - 13 T^{2} + \cdots + 13 \)
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|
| $41$ |
\( T^{3} - 18 T^{2} + \cdots + 8 \)
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| $43$ |
\( T^{3} - 5 T^{2} + \cdots - 29 \)
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|
| $47$ |
\( T^{3} - 2 T^{2} + \cdots - 104 \)
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|
| $53$ |
\( T^{3} - 28T - 56 \)
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|
| $59$ |
\( T^{3} + 8 T^{2} + \cdots - 1352 \)
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| $61$ |
\( T^{3} + T^{2} + \cdots + 181 \)
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| $67$ |
\( T^{3} - 2 T^{2} + \cdots - 104 \)
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| $71$ |
\( T^{3} - 8 T^{2} + \cdots + 1856 \)
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| $73$ |
\( T^{3} + 22 T^{2} + \cdots + 328 \)
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| $79$ |
\( T^{3} - 6 T^{2} + \cdots - 344 \)
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| $83$ |
\( T^{3} - 18 T^{2} + \cdots + 8 \)
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|
| $89$ |
\( T^{3} + 4 T^{2} + \cdots + 104 \)
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| $97$ |
\( T^{3} + 12 T^{2} + \cdots - 104 \)
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