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Properties

Label 1029.3.d.a
Level $1029$
Weight $3$
Character orbit 1029.d
Analytic conductor $28.038$
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] = [1029,3,Mod(685,1029)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1029, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1029.685"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1029 = 3 \cdot 7^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1029.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.0382192027\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 10 q^{2} + 50 q^{4} - 74 q^{8} - 72 q^{9} - 108 q^{11} + 66 q^{16} + 30 q^{18} + 88 q^{22} - 180 q^{23} - 56 q^{25} - 260 q^{29} + 120 q^{30} - 406 q^{32} - 150 q^{36} + 80 q^{37} + 84 q^{39} + 48 q^{43}+ \cdots + 324 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
685.1 −3.76772 1.73205i 10.1957 5.75271i − 6.52589i 0 −23.3438 −3.00000 − 21.6746i
685.2 −3.76772 − 1.73205i 10.1957 − 5.75271i 6.52589i 0 −23.3438 −3.00000 21.6746i
685.3 −3.70339 − 1.73205i 9.71513 3.29952i 6.41447i 0 −21.1654 −3.00000 − 12.2194i
685.4 −3.70339 1.73205i 9.71513 − 3.29952i − 6.41447i 0 −21.1654 −3.00000 12.2194i
685.5 −3.08503 − 1.73205i 5.51740 1.71685i 5.34343i 0 −4.68122 −3.00000 − 5.29652i
685.6 −3.08503 1.73205i 5.51740 − 1.71685i − 5.34343i 0 −4.68122 −3.00000 5.29652i
685.7 −2.08684 − 1.73205i 0.354888 − 5.90248i 3.61451i 0 7.60675 −3.00000 12.3175i
685.8 −2.08684 1.73205i 0.354888 5.90248i − 3.61451i 0 7.60675 −3.00000 − 12.3175i
685.9 −1.83663 − 1.73205i −0.626791 5.53860i 3.18114i 0 8.49770 −3.00000 − 10.1724i
685.10 −1.83663 1.73205i −0.626791 − 5.53860i − 3.18114i 0 8.49770 −3.00000 10.1724i
685.11 −0.780675 1.73205i −3.39055 − 4.60650i − 1.35217i 0 5.76962 −3.00000 3.59618i
685.12 −0.780675 − 1.73205i −3.39055 4.60650i 1.35217i 0 5.76962 −3.00000 − 3.59618i
685.13 −0.586446 1.73205i −3.65608 7.55868i − 1.01575i 0 4.48988 −3.00000 − 4.43275i
685.14 −0.586446 − 1.73205i −3.65608 − 7.55868i 1.01575i 0 4.48988 −3.00000 4.43275i
685.15 1.08149 − 1.73205i −2.83037 − 2.31032i − 1.87320i 0 −7.38700 −3.00000 − 2.49859i
685.16 1.08149 1.73205i −2.83037 2.31032i 1.87320i 0 −7.38700 −3.00000 2.49859i
685.17 1.40093 1.73205i −2.03741 6.74046i 2.42647i 0 −8.45796 −3.00000 9.44288i
685.18 1.40093 − 1.73205i −2.03741 − 6.74046i − 2.42647i 0 −8.45796 −3.00000 − 9.44288i
685.19 2.26112 1.73205i 1.11268 − 0.303238i 3.91638i 0 −6.52859 −3.00000 − 0.685659i
685.20 2.26112 − 1.73205i 1.11268 0.303238i − 3.91638i 0 −6.52859 −3.00000 0.685659i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 685.24
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1029.3.d.a ✓ 24
7.b odd 2 1 inner 1029.3.d.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1029.3.d.a ✓ 24 1.a even 1 1 trivial
1029.3.d.a ✓ 24 7.b odd 2 1 inner