![Copy content]()
gp:[N,k,chi] = [75,18,Mod(1,75)]
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("75.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 18, names="a")
Newform invariants
![Copy content]()
sage:traces = [2,-594]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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 \(\beta = 3\sqrt{14569}\).
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
|
| \(3\) |
\( +1 \) |
| \(5\) |
\( +1 \) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} + 594T_{2} - 42912 \)
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(75))\).
![Copy content]()
![Toggle raw display]()
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} + 594T - 42912 \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( (T + 6561)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{2} + \cdots + 36563624964160 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} + \cdots + 24\!\cdots\!72 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + \cdots + 85\!\cdots\!88 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} + \cdots + 23\!\cdots\!24 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} + \cdots - 18\!\cdots\!20 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} + \cdots - 22\!\cdots\!20 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + \cdots - 50\!\cdots\!80 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + \cdots + 37\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + \cdots - 41\!\cdots\!20 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + \cdots + 26\!\cdots\!40 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + \cdots - 36\!\cdots\!96 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + \cdots + 19\!\cdots\!36 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} + \cdots + 54\!\cdots\!20 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + \cdots - 17\!\cdots\!80 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} + \cdots + 19\!\cdots\!56 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} + \cdots + 27\!\cdots\!64 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots + 45\!\cdots\!64 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} + \cdots - 17\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} + \cdots - 10\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots + 36\!\cdots\!72 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots - 16\!\cdots\!60 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots + 81\!\cdots\!04 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
