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Properties

Label 543.4.a.c
Level $543$
Weight $4$
Character orbit 543.a
Self dual yes
Analytic conductor $32.038$
Analytic rank $0$
Dimension $23$
CM no
Inner twists $1$

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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] = [543,4,Mod(1,543)] 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("543.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(543, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 543 = 3 \cdot 181 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 543.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [23] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.0380371331\)
Analytic rank: \(0\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23 q + 7 q^{2} - 69 q^{3} + 79 q^{4} + 29 q^{5} - 21 q^{6} - 6 q^{7} + 84 q^{8} + 207 q^{9} + 41 q^{10} + 45 q^{11} - 237 q^{12} + 166 q^{13} - 23 q^{14} - 87 q^{15} + 195 q^{16} + 369 q^{17} + 63 q^{18}+ \cdots + 405 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.02333 −3.00000 17.2339 16.5758 15.0700 −1.10333 −46.3849 9.00000 −83.2660
1.2 −4.69142 −3.00000 14.0094 −0.689171 14.0743 −22.4545 −28.1926 9.00000 3.23319
1.3 −4.54651 −3.00000 12.6708 −8.97065 13.6395 −5.90620 −21.2358 9.00000 40.7852
1.4 −3.75976 −3.00000 6.13576 −9.67041 11.2793 15.6507 7.00907 9.00000 36.3584
1.5 −3.29875 −3.00000 2.88175 −8.81641 9.89625 −8.08600 16.8838 9.00000 29.0831
1.6 −2.94701 −3.00000 0.684851 5.16855 8.84102 16.7171 21.5578 9.00000 −15.2318
1.7 −1.97514 −3.00000 −4.09881 −9.26151 5.92543 −5.09750 23.8969 9.00000 18.2928
1.8 −1.87743 −3.00000 −4.47524 17.4027 5.63230 −18.1136 23.4214 9.00000 −32.6725
1.9 −1.65464 −3.00000 −5.26217 −5.80637 4.96392 33.3314 21.9441 9.00000 9.60744
1.10 −1.18302 −3.00000 −6.60046 9.11350 3.54907 13.9227 17.2727 9.00000 −10.7815
1.11 −0.121804 −3.00000 −7.98516 17.5835 0.365413 29.2994 1.94706 9.00000 −2.14174
1.12 0.324630 −3.00000 −7.89462 9.26331 −0.973891 −33.2631 −5.15988 9.00000 3.00715
1.13 1.50958 −3.00000 −5.72117 −3.71026 −4.52874 −6.88345 −20.7132 9.00000 −5.60093
1.14 1.72144 −3.00000 −5.03665 −0.851776 −5.16431 21.7289 −22.4418 9.00000 −1.46628
1.15 1.91929 −3.00000 −4.31632 −17.8997 −5.75788 −9.33325 −23.6386 9.00000 −34.3548
1.16 2.77838 −3.00000 −0.280580 20.2324 −8.33515 −17.8672 −23.0066 9.00000 56.2134
1.17 3.11841 −3.00000 1.72447 −16.2018 −9.35522 −33.3667 −19.5697 9.00000 −50.5239
1.18 3.24933 −3.00000 2.55813 −6.25884 −9.74799 −17.1743 −17.6824 9.00000 −20.3370
1.19 3.43854 −3.00000 3.82356 12.4060 −10.3156 28.0541 −14.3609 9.00000 42.6587
1.20 4.38501 −3.00000 11.2284 −19.8903 −13.1550 10.7284 14.1564 9.00000 −87.2194
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(181\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 543.4.a.c ✓ 23
3.b odd 2 1 1629.4.a.e 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
543.4.a.c ✓ 23 1.a even 1 1 trivial
1629.4.a.e 23 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{23} - 7 T_{2}^{22} - 107 T_{2}^{21} + 798 T_{2}^{20} + 4723 T_{2}^{19} - 38546 T_{2}^{18} + \cdots + 335321888 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(543))\). Copy content Toggle raw display