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gp:[N,k,chi] = [4563,2,Mod(1,4563)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4563, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
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magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4563.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
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sage:traces = [3,-2,0,0,-1,0,6,-3,0,-4,4,0,0,-4,0,2,-4,0,-2,0,0,9,-1,0,4,0,
0,7,16,0,-7,7,0,5,-16,0,0,-15,0,15,-1,0,-11]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(43)] == 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
|
| \(3\) |
\( +1 \) |
| \(13\) |
\( -1 \) |
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4563))\):
\( T_{2}^{3} + 2T_{2}^{2} - T_{2} - 1 \)
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\( T_{5}^{3} + T_{5}^{2} - 9T_{5} - 1 \)
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\( T_{7}^{3} - 6T_{7}^{2} + 5T_{7} + 13 \)
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\( T_{17}^{3} + 4T_{17}^{2} - 39T_{17} - 169 \)
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\( T_{19}^{3} + 2T_{19}^{2} - 29T_{19} + 13 \)
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\( T_{23}^{3} + T_{23}^{2} - 16T_{23} + 13 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} + 2T^{2} - T - 1 \)
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|
| $3$ |
\( T^{3} \)
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| $5$ |
\( T^{3} + T^{2} - 9T - 1 \)
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|
| $7$ |
\( T^{3} - 6 T^{2} + \cdots + 13 \)
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| $11$ |
\( T^{3} - 4 T^{2} + \cdots + 43 \)
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| $13$ |
\( T^{3} \)
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| $17$ |
\( T^{3} + 4 T^{2} + \cdots - 169 \)
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| $19$ |
\( T^{3} + 2 T^{2} + \cdots + 13 \)
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| $23$ |
\( T^{3} + T^{2} + \cdots + 13 \)
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| $29$ |
\( T^{3} - 16 T^{2} + \cdots - 104 \)
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| $31$ |
\( T^{3} + 7 T^{2} + \cdots - 91 \)
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| $37$ |
\( T^{3} - 49T - 91 \)
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| $41$ |
\( T^{3} + T^{2} + \cdots - 29 \)
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| $43$ |
\( T^{3} + 11 T^{2} + \cdots - 29 \)
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| $47$ |
\( T^{3} - 3 T^{2} + \cdots - 169 \)
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| $53$ |
\( T^{3} + 7 T^{2} + \cdots - 637 \)
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| $59$ |
\( T^{3} + 19 T^{2} + \cdots - 923 \)
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| $61$ |
\( T^{3} + 2 T^{2} + \cdots + 104 \)
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| $67$ |
\( T^{3} - 31 T^{2} + \cdots - 533 \)
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| $71$ |
\( T^{3} - 18 T^{2} + \cdots - 83 \)
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| $73$ |
\( T^{3} - 3 T^{2} + \cdots + 13 \)
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| $79$ |
\( T^{3} - 37 T^{2} + \cdots - 1469 \)
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| $83$ |
\( T^{3} + 4 T^{2} + \cdots - 1051 \)
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| $89$ |
\( T^{3} - 28 T^{2} + \cdots - 791 \)
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| $97$ |
\( T^{3} - 32 T^{2} + \cdots - 13 \)
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