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gp:[N,k,chi] = [483,4,Mod(1,483)]
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("483.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, 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,-4,9]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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
|
| \(3\) |
\( -1 \) |
| \(7\) |
\( +1 \) |
| \(23\) |
\( +1 \) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 4T_{2}^{2} - 8T_{2} - 1 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(483))\).
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| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} + 4 T^{2} + \cdots - 1 \)
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|
| $3$ |
\( (T - 3)^{3} \)
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|
| $5$ |
\( T^{3} - 2 T^{2} + \cdots - 133 \)
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|
| $7$ |
\( (T + 7)^{3} \)
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|
| $11$ |
\( T^{3} - 4 T^{2} + \cdots + 16888 \)
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|
| $13$ |
\( T^{3} - 32 T^{2} + \cdots + 7121 \)
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|
| $17$ |
\( T^{3} + 86 T^{2} + \cdots - 32140 \)
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|
| $19$ |
\( T^{3} - 32 T^{2} + \cdots - 4436 \)
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|
| $23$ |
\( (T + 23)^{3} \)
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|
| $29$ |
\( T^{3} + 341 T^{2} + \cdots + 1279711 \)
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|
| $31$ |
\( T^{3} + 452 T^{2} + \cdots + 2969438 \)
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|
| $37$ |
\( T^{3} + 183 T^{2} + \cdots - 3177991 \)
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|
| $41$ |
\( T^{3} - 175 T^{2} + \cdots + 11602699 \)
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|
| $43$ |
\( T^{3} + 320 T^{2} + \cdots - 3480943 \)
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|
| $47$ |
\( T^{3} + 71 T^{2} + \cdots - 30926812 \)
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|
| $53$ |
\( T^{3} - 27 T^{2} + \cdots + 9069176 \)
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|
| $59$ |
\( T^{3} + 1585 T^{2} + \cdots + 57554534 \)
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|
| $61$ |
\( T^{3} + 449 T^{2} + \cdots - 11531794 \)
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|
| $67$ |
\( T^{3} + 239 T^{2} + \cdots - 90556772 \)
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|
| $71$ |
\( T^{3} - 1255 T^{2} + \cdots + 7078618 \)
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| $73$ |
\( T^{3} + 342 T^{2} + \cdots + 20669796 \)
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|
| $79$ |
\( T^{3} - 994 T^{2} + \cdots + 161629604 \)
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|
| $83$ |
\( T^{3} + 1846 T^{2} + \cdots - 147725860 \)
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|
| $89$ |
\( T^{3} + \cdots - 1448227670 \)
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|
| $97$ |
\( T^{3} + 1797 T^{2} + \cdots + 26418199 \)
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