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gp:[N,k,chi] = [2205,4,Mod(1,2205)]
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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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,-2,0,14,15,0,0,-66,0,-10,20,0,0]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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
|
| \(3\) |
\( +1 \) |
| \(5\) |
\( -1 \) |
| \(7\) |
\( -1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2205))\):
\( T_{2}^{3} + 2T_{2}^{2} - 17T_{2} - 4 \)
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\( T_{11}^{3} - 20T_{11}^{2} - 2212T_{11} + 32160 \)
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\( T_{13}^{3} - 1748T_{13} + 17328 \)
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\( T_{17}^{3} - 234T_{17}^{2} + 15612T_{17} - 282328 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} + 2 T^{2} + \cdots - 4 \)
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|
| $3$ |
\( T^{3} \)
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| $5$ |
\( (T - 5)^{3} \)
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|
| $7$ |
\( T^{3} \)
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|
| $11$ |
\( T^{3} - 20 T^{2} + \cdots + 32160 \)
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|
| $13$ |
\( T^{3} - 1748T + 17328 \)
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|
| $17$ |
\( T^{3} - 234 T^{2} + \cdots - 282328 \)
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| $19$ |
\( T^{3} - 82 T^{2} + \cdots - 15280 \)
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| $23$ |
\( T^{3} + 30 T^{2} + \cdots + 378280 \)
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| $29$ |
\( T^{3} - 32 T^{2} + \cdots - 409600 \)
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| $31$ |
\( T^{3} - 362 T^{2} + \cdots - 1543664 \)
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| $37$ |
\( T^{3} - 302 T^{2} + \cdots + 1425496 \)
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| $41$ |
\( T^{3} - 626 T^{2} + \cdots + 16079208 \)
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| $43$ |
\( T^{3} + 68 T^{2} + \cdots - 10742464 \)
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| $47$ |
\( T^{3} - 936 T^{2} + \cdots - 29520128 \)
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| $53$ |
\( T^{3} + 298 T^{2} + \cdots - 19383056 \)
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| $59$ |
\( T^{3} - 428 T^{2} + \cdots + 229584064 \)
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| $61$ |
\( T^{3} + 1050 T^{2} + \cdots - 63221000 \)
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| $67$ |
\( T^{3} + 52 T^{2} + \cdots - 93054016 \)
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| $71$ |
\( T^{3} + 416 T^{2} + \cdots - 14345328 \)
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| $73$ |
\( T^{3} - 312 T^{2} + \cdots + 43935536 \)
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| $79$ |
\( T^{3} + 488 T^{2} + \cdots - 282894592 \)
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| $83$ |
\( T^{3} - 948 T^{2} + \cdots + 431507200 \)
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| $89$ |
\( T^{3} + 142 T^{2} + \cdots + 19655976 \)
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| $97$ |
\( T^{3} - 3052 T^{2} + \cdots - 204161472 \)
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