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Properties

Label 2720.2.f.d
Level $2720$
Weight $2$
Character orbit 2720.f
Analytic conductor $21.719$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2720,2,Mod(1361,2720)] 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("2720.1361"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2720, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2720 = 2^{5} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2720.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,0,0,0,0] 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
 
Self dual: no
Analytic conductor: \(21.7193093498\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 680)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 36 q^{9} - 8 q^{15} - 24 q^{17} - 24 q^{23} - 24 q^{25} - 24 q^{31} - 24 q^{33} + 72 q^{39} - 32 q^{41} + 8 q^{47} + 40 q^{49} + 24 q^{55} - 60 q^{57} + 56 q^{63} - 4 q^{65} - 20 q^{73} - 88 q^{79}+ \cdots - 52 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1361.1 0 − 3.36702i 0 − 1.00000i 0 2.13855 0 −8.33680 0
1361.2 0 − 3.27836i 0 − 1.00000i 0 −5.16742 0 −7.74765 0
1361.3 0 − 3.12736i 0 1.00000i 0 −1.48437 0 −6.78038 0
1361.4 0 − 2.68046i 0 − 1.00000i 0 1.61529 0 −4.18489 0
1361.5 0 − 2.47682i 0 1.00000i 0 0.433530 0 −3.13465 0
1361.6 0 − 1.97129i 0 − 1.00000i 0 −1.77965 0 −0.885992 0
1361.7 0 − 1.19072i 0 1.00000i 0 4.87818 0 1.58219 0
1361.8 0 − 1.11683i 0 1.00000i 0 1.39863 0 1.75269 0
1361.9 0 − 1.11462i 0 − 1.00000i 0 3.27408 0 1.75763 0
1361.10 0 − 0.956093i 0 1.00000i 0 −2.15752 0 2.08589 0
1361.11 0 − 0.272979i 0 − 1.00000i 0 −4.61360 0 2.92548 0
1361.12 0 − 0.183089i 0 − 1.00000i 0 1.46430 0 2.96648 0
1361.13 0 0.183089i 0 1.00000i 0 1.46430 0 2.96648 0
1361.14 0 0.272979i 0 1.00000i 0 −4.61360 0 2.92548 0
1361.15 0 0.956093i 0 − 1.00000i 0 −2.15752 0 2.08589 0
1361.16 0 1.11462i 0 1.00000i 0 3.27408 0 1.75763 0
1361.17 0 1.11683i 0 − 1.00000i 0 1.39863 0 1.75269 0
1361.18 0 1.19072i 0 − 1.00000i 0 4.87818 0 1.58219 0
1361.19 0 1.97129i 0 1.00000i 0 −1.77965 0 −0.885992 0
1361.20 0 2.47682i 0 − 1.00000i 0 0.433530 0 −3.13465 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1361.24
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2720.2.f.d 24
4.b odd 2 1 680.2.f.d ✓ 24
8.b even 2 1 inner 2720.2.f.d 24
8.d odd 2 1 680.2.f.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
680.2.f.d ✓ 24 4.b odd 2 1
680.2.f.d ✓ 24 8.d odd 2 1
2720.2.f.d 24 1.a even 1 1 trivial
2720.2.f.d 24 8.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2720, [\chi])\):

\( T_{3}^{24} + 54 T_{3}^{22} + 1233 T_{3}^{20} + 15528 T_{3}^{18} + 118160 T_{3}^{16} + 561296 T_{3}^{14} + \cdots + 1024 \) Copy content Toggle raw display
\( T_{7}^{12} - 52 T_{7}^{10} + 28 T_{7}^{9} + 872 T_{7}^{8} - 928 T_{7}^{7} - 5360 T_{7}^{6} + 7408 T_{7}^{5} + \cdots - 6656 \) Copy content Toggle raw display