![Copy content]()
gp:[N,k,chi] = [1058,6,Mod(1,1058)]
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("1058.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1058, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
Newform invariants
![Copy content]()
sage:traces = [2,8,-22,32,68]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
![Copy content]()
gp:f = lf[1] \\ Warning: the index may be different
![Copy content]()
sage:f.q_expansion() # note that sage often uses an isomorphic number field
![Copy content]()
gp:mfcoefs(f, 20)
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{2}\).
We also show the integral \(q\)-expansion of the trace form.
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
|
| \(2\) |
\( -1 \) |
| \(23\) |
\( -1 \) |
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 \(S_{6}^{\mathrm{new}}(\Gamma_0(1058))\):
\( T_{3}^{2} + 22T_{3} + 49 \)
![Copy content]()
![Toggle raw display]()
|
\( T_{5}^{2} - 68T_{5} - 3844 \)
![Copy content]()
![Toggle raw display]()
|
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T - 4)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( T^{2} + 22T + 49 \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{2} - 68T - 3844 \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{2} - 312T + 22024 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} - 12T - 488036 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + 1482 T + 548569 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} + 1768 T - 137912 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} - 1124T - 17084 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + 5118 T - 23996447 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + 3110 T - 2069983 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + 36 T - 166713476 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + 7234 T + 8654401 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + 28816 T + 184252352 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + 19918 T + 96499753 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} - 8508 T - 506524316 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + 46944 T + 548298976 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} - 61860 T + 551109700 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} - 25428 T - 312058404 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots - 2668148783 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} - 11610 T - 392388407 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} - 11340 T - 943610588 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots - 2420534536 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots + 3214870000 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots + 1114766072 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
