![Copy content]()
gp:[N,k,chi] = [225,10,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
![Copy content]()
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Newform invariants
![Copy content]()
sage:traces = [2,-36,0,256,0,0,-3318]
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
![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 \(\beta = 2\sqrt{79}\).
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 intersection of the kernels of the following linear operators acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(225))\):
\( T_{2}^{2} + 36T_{2} + 8 \)
![Copy content]()
![Toggle raw display]()
|
\( T_{7}^{2} + 3318T_{7} - 2264535 \)
![Copy content]()
![Toggle raw display]()
|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} + 36T + 8 \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{2} + 3318 T - 2264535 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} + \cdots - 1089595948 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + \cdots - 2534298407 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} + \cdots - 90389270476 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} + \cdots + 273466881505 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} + \cdots - 1307719531980 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + \cdots - 290780819500 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + \cdots - 38000674643175 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + \cdots - 47108368408220 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + \cdots - 214074226693600 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + \cdots - 993179978760551 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + \cdots + 789343287059876 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} + \cdots - 180915167344240 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + \cdots - 11\!\cdots\!20 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} + \cdots + 13\!\cdots\!21 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} + \cdots + 24\!\cdots\!89 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots - 25\!\cdots\!56 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} + \cdots - 17\!\cdots\!80 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} + \cdots + 61\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots - 22\!\cdots\!68 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots - 18\!\cdots\!80 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots + 75\!\cdots\!29 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
