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Properties

Label 546.4.s.d
Level $546$
Weight $4$
Character orbit 546.s
Analytic conductor $32.215$
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] = [546,4,Mod(43,546)] 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("546.43"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(32.2150428631\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 36 q^{3} + 48 q^{4} - 108 q^{9} - 24 q^{10} - 174 q^{11} + 288 q^{12} - 96 q^{13} - 336 q^{14} - 90 q^{15} - 192 q^{16} + 140 q^{17} - 60 q^{19} + 120 q^{20} - 128 q^{22} + 34 q^{23} - 1004 q^{25}+ \cdots - 3936 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
43.1 −1.73205 − 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 20.8505i −5.19615 + 3.00000i 6.06218 − 3.50000i − 8.00000i −4.50000 − 7.79423i −20.8505 + 36.1141i
43.2 −1.73205 − 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 9.97677i −5.19615 + 3.00000i 6.06218 − 3.50000i − 8.00000i −4.50000 − 7.79423i −9.97677 + 17.2803i
43.3 −1.73205 − 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 10.6352i −5.19615 + 3.00000i 6.06218 − 3.50000i − 8.00000i −4.50000 − 7.79423i −10.6352 + 18.4208i
43.4 −1.73205 − 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 2.48320i −5.19615 + 3.00000i 6.06218 − 3.50000i − 8.00000i −4.50000 − 7.79423i −2.48320 + 4.30102i
43.5 −1.73205 − 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i 11.2847i −5.19615 + 3.00000i 6.06218 − 3.50000i − 8.00000i −4.50000 − 7.79423i 11.2847 − 19.5457i
43.6 −1.73205 − 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i 18.0007i −5.19615 + 3.00000i 6.06218 − 3.50000i − 8.00000i −4.50000 − 7.79423i 18.0007 − 31.1782i
43.7 1.73205 + 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 22.1146i 5.19615 − 3.00000i −6.06218 + 3.50000i 8.00000i −4.50000 − 7.79423i 22.1146 − 38.3036i
43.8 1.73205 + 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 3.23892i 5.19615 − 3.00000i −6.06218 + 3.50000i 8.00000i −4.50000 − 7.79423i 3.23892 − 5.60997i
43.9 1.73205 + 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 0.0691052i 5.19615 − 3.00000i −6.06218 + 3.50000i 8.00000i −4.50000 − 7.79423i 0.0691052 − 0.119694i
43.10 1.73205 + 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i − 1.79706i 5.19615 − 3.00000i −6.06218 + 3.50000i 8.00000i −4.50000 − 7.79423i 1.79706 − 3.11260i
43.11 1.73205 + 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i 5.47106i 5.19615 − 3.00000i −6.06218 + 3.50000i 8.00000i −4.50000 − 7.79423i −5.47106 + 9.47616i
43.12 1.73205 + 1.00000i 1.50000 − 2.59808i 2.00000 + 3.46410i 19.0883i 5.19615 − 3.00000i −6.06218 + 3.50000i 8.00000i −4.50000 − 7.79423i −19.0883 + 33.0620i
127.1 −1.73205 + 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i 20.8505i −5.19615 − 3.00000i 6.06218 + 3.50000i 8.00000i −4.50000 + 7.79423i −20.8505 − 36.1141i
127.2 −1.73205 + 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i 9.97677i −5.19615 − 3.00000i 6.06218 + 3.50000i 8.00000i −4.50000 + 7.79423i −9.97677 − 17.2803i
127.3 −1.73205 + 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i 10.6352i −5.19615 − 3.00000i 6.06218 + 3.50000i 8.00000i −4.50000 + 7.79423i −10.6352 − 18.4208i
127.4 −1.73205 + 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i 2.48320i −5.19615 − 3.00000i 6.06218 + 3.50000i 8.00000i −4.50000 + 7.79423i −2.48320 − 4.30102i
127.5 −1.73205 + 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i − 11.2847i −5.19615 − 3.00000i 6.06218 + 3.50000i 8.00000i −4.50000 + 7.79423i 11.2847 + 19.5457i
127.6 −1.73205 + 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i − 18.0007i −5.19615 − 3.00000i 6.06218 + 3.50000i 8.00000i −4.50000 + 7.79423i 18.0007 + 31.1782i
127.7 1.73205 − 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i 22.1146i 5.19615 + 3.00000i −6.06218 − 3.50000i − 8.00000i −4.50000 + 7.79423i 22.1146 + 38.3036i
127.8 1.73205 − 1.00000i 1.50000 + 2.59808i 2.00000 − 3.46410i 3.23892i 5.19615 + 3.00000i −6.06218 − 3.50000i − 8.00000i −4.50000 + 7.79423i 3.23892 + 5.60997i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 43.12
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.e even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 546.4.s.d ✓ 24
13.e even 6 1 inner 546.4.s.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.4.s.d ✓ 24 1.a even 1 1 trivial
546.4.s.d ✓ 24 13.e even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} + 2002 T_{5}^{22} + 1651051 T_{5}^{20} + 726081706 T_{5}^{18} + 184680126175 T_{5}^{16} + \cdots + 10\!\cdots\!64 \) acting on \(S_{4}^{\mathrm{new}}(546, [\chi])\). Copy content Toggle raw display