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Properties

Label 546.4.s.c
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 36 q^{3} + 48 q^{4} - 108 q^{9} + 32 q^{10} + 54 q^{11} - 288 q^{12} - 80 q^{13} + 336 q^{14} + 18 q^{15} - 192 q^{16} + 256 q^{17} + 60 q^{19} + 24 q^{20} + 40 q^{22} - 26 q^{23} - 1004 q^{25} - 128 q^{26}+ \cdots + 984 q^{97}+O(q^{100}) \) 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 − 16.8117i 5.19615 − 3.00000i −6.06218 + 3.50000i − 8.00000i −4.50000 − 7.79423i −16.8117 + 29.1187i
43.2 −1.73205 − 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i − 3.21341i 5.19615 − 3.00000i −6.06218 + 3.50000i − 8.00000i −4.50000 − 7.79423i −3.21341 + 5.56579i
43.3 −1.73205 − 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i − 10.5379i 5.19615 − 3.00000i −6.06218 + 3.50000i − 8.00000i −4.50000 − 7.79423i −10.5379 + 18.2521i
43.4 −1.73205 − 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i 5.00822i 5.19615 − 3.00000i −6.06218 + 3.50000i − 8.00000i −4.50000 − 7.79423i 5.00822 − 8.67449i
43.5 −1.73205 − 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i 11.1793i 5.19615 − 3.00000i −6.06218 + 3.50000i − 8.00000i −4.50000 − 7.79423i 11.1793 − 19.3632i
43.6 −1.73205 − 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i 20.6434i 5.19615 − 3.00000i −6.06218 + 3.50000i − 8.00000i −4.50000 − 7.79423i 20.6434 − 35.7554i
43.7 1.73205 + 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i − 20.8745i −5.19615 + 3.00000i 6.06218 − 3.50000i 8.00000i −4.50000 − 7.79423i 20.8745 − 36.1557i
43.8 1.73205 + 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i 12.4907i −5.19615 + 3.00000i 6.06218 − 3.50000i 8.00000i −4.50000 − 7.79423i −12.4907 + 21.6344i
43.9 1.73205 + 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i − 11.8865i −5.19615 + 3.00000i 6.06218 − 3.50000i 8.00000i −4.50000 − 7.79423i 11.8865 − 20.5881i
43.10 1.73205 + 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i − 2.71992i −5.19615 + 3.00000i 6.06218 − 3.50000i 8.00000i −4.50000 − 7.79423i 2.71992 − 4.71103i
43.11 1.73205 + 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i − 3.20568i −5.19615 + 3.00000i 6.06218 − 3.50000i 8.00000i −4.50000 − 7.79423i 3.20568 − 5.55239i
43.12 1.73205 + 1.00000i −1.50000 + 2.59808i 2.00000 + 3.46410i 16.4639i −5.19615 + 3.00000i 6.06218 − 3.50000i 8.00000i −4.50000 − 7.79423i −16.4639 + 28.5163i
127.1 −1.73205 + 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i 16.8117i 5.19615 + 3.00000i −6.06218 − 3.50000i 8.00000i −4.50000 + 7.79423i −16.8117 − 29.1187i
127.2 −1.73205 + 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i 3.21341i 5.19615 + 3.00000i −6.06218 − 3.50000i 8.00000i −4.50000 + 7.79423i −3.21341 − 5.56579i
127.3 −1.73205 + 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i 10.5379i 5.19615 + 3.00000i −6.06218 − 3.50000i 8.00000i −4.50000 + 7.79423i −10.5379 − 18.2521i
127.4 −1.73205 + 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i − 5.00822i 5.19615 + 3.00000i −6.06218 − 3.50000i 8.00000i −4.50000 + 7.79423i 5.00822 + 8.67449i
127.5 −1.73205 + 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i − 11.1793i 5.19615 + 3.00000i −6.06218 − 3.50000i 8.00000i −4.50000 + 7.79423i 11.1793 + 19.3632i
127.6 −1.73205 + 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i − 20.6434i 5.19615 + 3.00000i −6.06218 − 3.50000i 8.00000i −4.50000 + 7.79423i 20.6434 + 35.7554i
127.7 1.73205 − 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i 20.8745i −5.19615 − 3.00000i 6.06218 + 3.50000i − 8.00000i −4.50000 + 7.79423i 20.8745 + 36.1557i
127.8 1.73205 − 1.00000i −1.50000 − 2.59808i 2.00000 − 3.46410i − 12.4907i −5.19615 − 3.00000i 6.06218 + 3.50000i − 8.00000i −4.50000 + 7.79423i −12.4907 − 21.6344i
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.c ✓ 24
13.e even 6 1 inner 546.4.s.c ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
546.4.s.c ✓ 24 1.a even 1 1 trivial
546.4.s.c ✓ 24 13.e even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} + 2002 T_{5}^{22} + 1705011 T_{5}^{20} + 809616322 T_{5}^{18} + 236166669391 T_{5}^{16} + \cdots + 85\!\cdots\!56 \) acting on \(S_{4}^{\mathrm{new}}(546, [\chi])\). Copy content Toggle raw display