![Copy content]()
gp:[N,k,chi] = [968,4,Mod(1,968)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("968.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(968, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
Newform invariants
![Copy content]()
sage:traces = [3,0,2,0,-9,0,-6]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
![Copy content]()
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.
![Copy content]()
gp:mfembed(f)
| \( p \) |
Sign
|
| \(2\) |
\( -1 \) |
| \(11\) |
\( -1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(968))\):
\( T_{3}^{3} - 2T_{3}^{2} - 36T_{3} + 88 \)
![Copy content]()
![Toggle raw display]()
|
\( T_{7}^{3} + 6T_{7}^{2} - 212T_{7} + 664 \)
![Copy content]()
![Toggle raw display]()
|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( T^{3} - 2 T^{2} + \cdots + 88 \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{3} + 9 T^{2} + \cdots + 459 \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{3} + 6 T^{2} + \cdots + 664 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{3} \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{3} - 17 T^{2} + \cdots + 93 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{3} + 17 T^{2} + \cdots - 65981 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{3} + 6 T^{2} + \cdots - 274024 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{3} - 106 T^{2} + \cdots + 153656 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{3} + 55 T^{2} + \cdots - 712827 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{3} + 58 T^{2} + \cdots - 941208 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{3} + 277 T^{2} + \cdots - 14080649 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{3} - 439 T^{2} + \cdots + 46740443 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{3} + 160 T^{2} + \cdots + 3465856 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{3} + 86 T^{2} + \cdots - 46969224 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{3} - 687 T^{2} + \cdots + 23674099 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{3} - 56 T^{2} + \cdots - 4619648 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{3} - 502 T^{2} + \cdots + 44138552 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{3} - 882 T^{2} + \cdots + 32178168 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{3} + 1236 T^{2} + \cdots - 113556032 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{3} - 502 T^{2} + \cdots + 402393144 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{3} - 2706 T^{2} + \cdots - 667322216 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{3} - 858 T^{2} + \cdots + 381691288 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{3} - 1341 T^{2} + \cdots + 15338369 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{3} - 2953 T^{2} + \cdots + 297518597 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
