![Copy content]()
gp:[N,k,chi] = [2400,4,Mod(1,2400)]
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("2400.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
Newform invariants
![Copy content]()
sage:traces = [3,0,9,0,0,0,9,0,27,0,-4,0,-7]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( -1 \) |
| \(5\) |
\( +1 \) |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2400))\):
\( T_{7}^{3} - 9T_{7}^{2} - 629T_{7} - 4299 \)
![Copy content]()
![Toggle raw display]()
|
\( T_{11}^{3} + 4T_{11}^{2} - 2480T_{11} + 18400 \)
![Copy content]()
![Toggle raw display]()
|
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{3} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( (T - 3)^{3} \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{3} \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{3} - 9 T^{2} + \cdots - 4299 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{3} + 4 T^{2} + \cdots + 18400 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{3} + 7 T^{2} + \cdots + 62933 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{3} - 20 T^{2} + \cdots - 81760 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{3} - 41 T^{2} + \cdots - 50715 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{3} - 40 T^{2} + \cdots + 9056 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{3} - 48 T^{2} + \cdots + 3736800 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{3} + 81 T^{2} + \cdots - 1203117 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{3} - 66 T^{2} + \cdots + 1856744 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{3} - 254 T^{2} + \cdots + 10242744 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{3} - 293 T^{2} + \cdots + 5155929 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{3} - 318 T^{2} + \cdots + 18003864 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{3} + 282 T^{2} + \cdots - 130493160 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{3} - 102 T^{2} + \cdots + 59666040 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{3} - 913 T^{2} + \cdots + 60095965 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{3} - 153 T^{2} + \cdots - 5619435 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{3} - 162 T^{2} + \cdots - 34620408 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{3} + 566 T^{2} + \cdots - 366895800 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{3} + 1160 T^{2} + \cdots + 44658176 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{3} - 914 T^{2} + \cdots + 156728104 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{3} - 1232 T^{2} + \cdots + 1095680 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{3} - 2089 T^{2} + \cdots + 206116549 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
