↑

Properties

Label 4896.2.j.a
Level $4896$
Weight $2$
Character orbit 4896.j
Analytic conductor $39.095$
Analytic rank $0$
Dimension $64$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [4896,2,Mod(1871,4896)] 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("4896.1871"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4896, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 4896 = 2^{5} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4896.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(39.0947568296\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: no (minimal twist has level 1224)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 64 q^{25} + 64 q^{43} - 32 q^{49} - 32 q^{67} + 32 q^{73} - 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Embeddings

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 comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1871.1 0 0 0 −4.13342 0 3.97831i 0 0 0
1871.2 0 0 0 −4.13342 0 − 3.97831i 0 0 0
1871.3 0 0 0 −3.84894 0 0.134897i 0 0 0
1871.4 0 0 0 −3.84894 0 − 0.134897i 0 0 0
1871.5 0 0 0 −3.64894 0 1.71621i 0 0 0
1871.6 0 0 0 −3.64894 0 − 1.71621i 0 0 0
1871.7 0 0 0 −3.57638 0 − 3.75208i 0 0 0
1871.8 0 0 0 −3.57638 0 3.75208i 0 0 0
1871.9 0 0 0 −3.39717 0 2.62431i 0 0 0
1871.10 0 0 0 −3.39717 0 − 2.62431i 0 0 0
1871.11 0 0 0 −2.92803 0 0.694845i 0 0 0
1871.12 0 0 0 −2.92803 0 − 0.694845i 0 0 0
1871.13 0 0 0 −2.17977 0 − 2.09778i 0 0 0
1871.14 0 0 0 −2.17977 0 2.09778i 0 0 0
1871.15 0 0 0 −1.92308 0 − 3.93404i 0 0 0
1871.16 0 0 0 −1.92308 0 3.93404i 0 0 0
1871.17 0 0 0 −1.44941 0 − 0.677387i 0 0 0
1871.18 0 0 0 −1.44941 0 0.677387i 0 0 0
1871.19 0 0 0 −1.43325 0 − 0.898362i 0 0 0
1871.20 0 0 0 −1.43325 0 0.898362i 0 0 0
See all 64 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1871.64
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.d odd 2 1 inner
24.f even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4896.2.j.a 64
3.b odd 2 1 inner 4896.2.j.a 64
4.b odd 2 1 1224.2.j.a ✓ 64
8.b even 2 1 1224.2.j.a ✓ 64
8.d odd 2 1 inner 4896.2.j.a 64
12.b even 2 1 1224.2.j.a ✓ 64
24.f even 2 1 inner 4896.2.j.a 64
24.h odd 2 1 1224.2.j.a ✓ 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1224.2.j.a ✓ 64 4.b odd 2 1
1224.2.j.a ✓ 64 8.b even 2 1
1224.2.j.a ✓ 64 12.b even 2 1
1224.2.j.a ✓ 64 24.h odd 2 1
4896.2.j.a 64 1.a even 1 1 trivial
4896.2.j.a 64 3.b odd 2 1 inner
4896.2.j.a 64 8.d odd 2 1 inner
4896.2.j.a 64 24.f even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(4896, [\chi])\).