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gp:[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, 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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
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sage:traces = [3,3,0,3,1,0,9,3,0,1,-6]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( -1 \) |
| \(223\) |
\( -1 \) |
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\):
\( T_{5}^{3} - T_{5}^{2} - 8T_{5} + 11 \)
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\( T_{7}^{3} - 9T_{7}^{2} + 22T_{7} - 11 \)
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\( T_{11}^{3} + 6T_{11}^{2} + 7T_{11} - 3 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T - 1)^{3} \)
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|
| $3$ |
\( T^{3} \)
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|
| $5$ |
\( T^{3} - T^{2} - 8T + 11 \)
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|
| $7$ |
\( T^{3} - 9 T^{2} + \cdots - 11 \)
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|
| $11$ |
\( T^{3} + 6 T^{2} + \cdots - 3 \)
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|
| $13$ |
\( T^{3} - 11 T^{2} + \cdots - 27 \)
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|
| $17$ |
\( T^{3} - 2 T^{2} + \cdots + 55 \)
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|
| $19$ |
\( T^{3} - 5 T^{2} + \cdots + 15 \)
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|
| $23$ |
\( T^{3} - 2 T^{2} + \cdots + 75 \)
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| $29$ |
\( T^{3} - 9 T^{2} + \cdots - 13 \)
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| $31$ |
\( T^{3} + 5 T^{2} + \cdots - 169 \)
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| $37$ |
\( T^{3} - 4 T^{2} + \cdots + 709 \)
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| $41$ |
\( T^{3} + 8 T^{2} + \cdots - 555 \)
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| $43$ |
\( T^{3} - 2 T^{2} + \cdots + 129 \)
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| $47$ |
\( T^{3} - 11 T^{2} + \cdots + 153 \)
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| $53$ |
\( T^{3} + 3 T^{2} + \cdots - 289 \)
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| $59$ |
\( T^{3} - 6 T^{2} + \cdots - 81 \)
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| $61$ |
\( T^{3} + T^{2} + \cdots - 585 \)
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| $67$ |
\( T^{3} - 15T^{2} + 473 \)
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| $71$ |
\( T^{3} - 15 T^{2} + \cdots - 33 \)
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| $73$ |
\( T^{3} + 4 T^{2} + \cdots + 121 \)
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| $79$ |
\( T^{3} - 22 T^{2} + \cdots + 1089 \)
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| $83$ |
\( T^{3} + 15 T^{2} + \cdots - 999 \)
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| $89$ |
\( T^{3} + 3 T^{2} + \cdots - 2151 \)
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| $97$ |
\( T^{3} + T^{2} + \cdots + 219 \)
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