Properties

Label 6624.2.j.b
Level $6624$
Weight $2$
Character orbit 6624.j
Analytic conductor $52.893$
Analytic rank $0$
Dimension $44$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [6624,2,Mod(4463,6624)] 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("6624.4463"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6624, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 6624 = 2^{5} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6624.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [44,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(52.8929062989\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: no (minimal twist has level 1656)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 44 q^{23} + 44 q^{25} + 32 q^{43} - 28 q^{49} + 32 q^{71} + 16 q^{73} + 48 q^{91} - 32 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4463.1 0 0 0 −3.80620 0 − 3.81123i 0 0 0
4463.2 0 0 0 −3.80620 0 3.81123i 0 0 0
4463.3 0 0 0 −3.77918 0 1.51839i 0 0 0
4463.4 0 0 0 −3.77918 0 − 1.51839i 0 0 0
4463.5 0 0 0 −2.98164 0 0.0431221i 0 0 0
4463.6 0 0 0 −2.98164 0 − 0.0431221i 0 0 0
4463.7 0 0 0 −2.79250 0 0.430435i 0 0 0
4463.8 0 0 0 −2.79250 0 − 0.430435i 0 0 0
4463.9 0 0 0 −2.72499 0 3.57690i 0 0 0
4463.10 0 0 0 −2.72499 0 − 3.57690i 0 0 0
4463.11 0 0 0 −2.14897 0 3.00283i 0 0 0
4463.12 0 0 0 −2.14897 0 − 3.00283i 0 0 0
4463.13 0 0 0 −1.55795 0 1.45917i 0 0 0
4463.14 0 0 0 −1.55795 0 − 1.45917i 0 0 0
4463.15 0 0 0 −1.21248 0 − 1.16832i 0 0 0
4463.16 0 0 0 −1.21248 0 1.16832i 0 0 0
4463.17 0 0 0 −0.931091 0 − 4.48146i 0 0 0
4463.18 0 0 0 −0.931091 0 4.48146i 0 0 0
4463.19 0 0 0 −0.320428 0 0.312552i 0 0 0
4463.20 0 0 0 −0.320428 0 − 0.312552i 0 0 0
See all 44 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 4463.44
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
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 6624.2.j.b 44
3.b odd 2 1 6624.2.j.a 44
4.b odd 2 1 1656.2.j.a ✓ 44
8.b even 2 1 1656.2.j.b yes 44
8.d odd 2 1 6624.2.j.a 44
12.b even 2 1 1656.2.j.b yes 44
24.f even 2 1 inner 6624.2.j.b 44
24.h odd 2 1 1656.2.j.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1656.2.j.a ✓ 44 4.b odd 2 1
1656.2.j.a ✓ 44 24.h odd 2 1
1656.2.j.b yes 44 8.b even 2 1
1656.2.j.b yes 44 12.b even 2 1
6624.2.j.a 44 3.b odd 2 1
6624.2.j.a 44 8.d odd 2 1
6624.2.j.b 44 1.a even 1 1 trivial
6624.2.j.b 44 24.f even 2 1 inner