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gp:[N,k,chi] = [1232,4,Mod(1,1232)]
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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
Newform invariants
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sage:traces = [3,0,-6,0,26]
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
|
| \(2\) |
\( -1 \) |
| \(7\) |
\( -1 \) |
| \(11\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1232))\):
\( T_{3}^{3} + 6T_{3}^{2} - 52T_{3} - 264 \)
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\( T_{5}^{3} - 26T_{5}^{2} + 60T_{5} + 648 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
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| $3$ |
\( T^{3} + 6 T^{2} + \cdots - 264 \)
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|
| $5$ |
\( T^{3} - 26 T^{2} + \cdots + 648 \)
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|
| $7$ |
\( (T - 7)^{3} \)
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|
| $11$ |
\( (T + 11)^{3} \)
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|
| $13$ |
\( T^{3} - 72 T^{2} + \cdots + 331632 \)
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|
| $17$ |
\( T^{3} - 56 T^{2} + \cdots + 88976 \)
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| $19$ |
\( T^{3} - 48 T^{2} + \cdots - 28512 \)
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| $23$ |
\( T^{3} - 244 T^{2} + \cdots - 219584 \)
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| $29$ |
\( T^{3} - 198 T^{2} + \cdots + 3523896 \)
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| $31$ |
\( T^{3} + 374 T^{2} + \cdots - 15721176 \)
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| $37$ |
\( T^{3} - 110 T^{2} + \cdots + 5981784 \)
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| $41$ |
\( T^{3} + 648 T^{2} + \cdots - 28837872 \)
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| $43$ |
\( T^{3} - 500 T^{2} + \cdots + 2503232 \)
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| $47$ |
\( T^{3} - 326 T^{2} + \cdots + 136297368 \)
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| $53$ |
\( T^{3} - 206 T^{2} + \cdots + 863064 \)
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| $59$ |
\( T^{3} - 266 T^{2} + \cdots + 4809816 \)
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| $61$ |
\( T^{3} - 308 T^{2} + \cdots + 81057168 \)
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| $67$ |
\( T^{3} + 256 T^{2} + \cdots + 1711488 \)
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| $71$ |
\( T^{3} - 484 T^{2} + \cdots + 19953216 \)
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| $73$ |
\( T^{3} + 1028 T^{2} + \cdots - 550878192 \)
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| $79$ |
\( T^{3} - 1072 T^{2} + \cdots + 148401792 \)
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| $83$ |
\( T^{3} + 912 T^{2} + \cdots - 33774048 \)
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| $89$ |
\( T^{3} + \cdots - 1452062376 \)
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| $97$ |
\( T^{3} - 2042 T^{2} + \cdots - 259709688 \)
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