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gp:[N,k,chi] = [1360,4,Mod(1,1360)]
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("1360.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1360, 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,-9,0,-15,0,-34,0,60,0,-52]
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
|
| \(2\) |
\( -1 \) |
| \(5\) |
\( +1 \) |
| \(17\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1360))\):
\( T_{3}^{3} + 9T_{3}^{2} - 30T_{3} - 254 \)
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\( T_{7}^{3} + 34T_{7}^{2} + 50T_{7} - 44 \)
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\( T_{11}^{3} + 52T_{11}^{2} + 262T_{11} - 6784 \)
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|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
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| $3$ |
\( T^{3} + 9 T^{2} + \cdots - 254 \)
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|
| $5$ |
\( (T + 5)^{3} \)
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| $7$ |
\( T^{3} + 34 T^{2} + \cdots - 44 \)
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| $11$ |
\( T^{3} + 52 T^{2} + \cdots - 6784 \)
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| $13$ |
\( T^{3} - 19 T^{2} + \cdots + 20408 \)
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| $17$ |
\( (T + 17)^{3} \)
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| $19$ |
\( T^{3} - 153 T^{2} + \cdots + 43112 \)
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| $23$ |
\( T^{3} + 162 T^{2} + \cdots - 587260 \)
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| $29$ |
\( T^{3} - 45 T^{2} + \cdots - 1563820 \)
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| $31$ |
\( T^{3} - 67 T^{2} + \cdots - 634 \)
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| $37$ |
\( T^{3} + 308 T^{2} + \cdots - 879328 \)
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| $41$ |
\( T^{3} - 498 T^{2} + \cdots + 948856 \)
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| $43$ |
\( T^{3} - 246 T^{2} + \cdots + 8063768 \)
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| $47$ |
\( T^{3} + 101 T^{2} + \cdots + 37575724 \)
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| $53$ |
\( T^{3} - 893 T^{2} + \cdots - 23102788 \)
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| $59$ |
\( T^{3} + 355 T^{2} + \cdots - 23789032 \)
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| $61$ |
\( T^{3} - 1019 T^{2} + \cdots - 32261500 \)
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| $67$ |
\( T^{3} + 334 T^{2} + \cdots - 2242600 \)
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| $71$ |
\( T^{3} + 313 T^{2} + \cdots + 104660798 \)
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| $73$ |
\( T^{3} - 639 T^{2} + \cdots - 23564196 \)
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| $79$ |
\( T^{3} - 92 T^{2} + \cdots - 310900832 \)
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| $83$ |
\( T^{3} + 2736 T^{2} + \cdots + 751119952 \)
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| $89$ |
\( T^{3} - 1623 T^{2} + \cdots + 25616512 \)
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| $97$ |
\( T^{3} + 475 T^{2} + \cdots - 473709668 \)
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