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Properties

Label 567.2.be.a
Level $567$
Weight $2$
Character orbit 567.be
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $4$

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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] = [567,2,Mod(62,567)] 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("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.be (of order \(18\), degree \(6\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
62.1 −0.924066 − 2.53885i 0 −4.05977 + 3.40655i −0.268129 − 1.52064i 0 −1.64503 + 2.07217i 7.72059 + 4.45748i 0 −3.61290 + 2.08591i
62.2 −0.924066 − 2.53885i 0 −4.05977 + 3.40655i 0.268129 + 1.52064i 0 1.75503 − 1.97986i 7.72059 + 4.45748i 0 3.61290 − 2.08591i
62.3 −0.735125 − 2.01974i 0 −2.00685 + 1.68395i −0.0677816 − 0.384409i 0 0.618456 + 2.57245i 1.15362 + 0.666045i 0 −0.726578 + 0.419490i
62.4 −0.735125 − 2.01974i 0 −2.00685 + 1.68395i 0.0677816 + 0.384409i 0 2.64076 + 0.162359i 1.15362 + 0.666045i 0 0.726578 − 0.419490i
62.5 −0.492726 − 1.35375i 0 −0.0577819 + 0.0484848i −0.440273 − 2.49691i 0 −1.60923 − 2.10009i −2.40115 − 1.38630i 0 −3.16327 + 1.82631i
62.6 −0.492726 − 1.35375i 0 −0.0577819 + 0.0484848i 0.440273 + 2.49691i 0 −2.34762 − 1.22011i −2.40115 − 1.38630i 0 3.16327 − 1.82631i
62.7 −0.471430 − 1.29524i 0 0.0766803 − 0.0643424i −0.459149 − 2.60396i 0 1.90985 − 1.83097i −2.50689 − 1.44736i 0 −3.15631 + 1.82230i
62.8 −0.471430 − 1.29524i 0 0.0766803 − 0.0643424i 0.459149 + 2.60396i 0 −1.47152 + 2.19878i −2.50689 − 1.44736i 0 3.15631 − 1.82230i
62.9 −0.157445 − 0.432576i 0 1.36976 − 1.14936i −0.725040 − 4.11191i 0 −1.09969 + 2.40638i −1.51017 − 0.871900i 0 −1.66456 + 0.961033i
62.10 −0.157445 − 0.432576i 0 1.36976 − 1.14936i 0.725040 + 4.11191i 0 2.17886 − 1.50085i −1.51017 − 0.871900i 0 1.66456 − 0.961033i
62.11 0.0448460 + 0.123213i 0 1.51892 − 1.27452i −0.231324 − 1.31190i 0 −0.772696 − 2.53040i 0.452264 + 0.261115i 0 0.151270 − 0.0873359i
62.12 0.0448460 + 0.123213i 0 1.51892 − 1.27452i 0.231324 + 1.31190i 0 −2.62614 − 0.321557i 0.452264 + 0.261115i 0 −0.151270 + 0.0873359i
62.13 0.234777 + 0.645045i 0 1.17113 − 0.982692i −0.231854 − 1.31491i 0 1.38106 + 2.25670i 2.09779 + 1.21116i 0 0.793741 − 0.458267i
62.14 0.234777 + 0.645045i 0 1.17113 − 0.982692i 0.231854 + 1.31491i 0 2.46223 + 0.968204i 2.09779 + 1.21116i 0 −0.793741 + 0.458267i
62.15 0.422526 + 1.16088i 0 0.362974 − 0.304571i −0.253991 − 1.44045i 0 1.07486 − 2.41758i 2.64668 + 1.52806i 0 1.56488 − 0.903482i
62.16 0.422526 + 1.16088i 0 0.362974 − 0.304571i 0.253991 + 1.44045i 0 −2.19420 + 1.47834i 2.64668 + 1.52806i 0 −1.56488 + 0.903482i
62.17 0.681310 + 1.87188i 0 −1.50768 + 1.26509i −0.291735 − 1.65451i 0 0.496759 − 2.59870i 0.0549773 + 0.0317412i 0 2.89829 − 1.67333i
62.18 0.681310 + 1.87188i 0 −1.50768 + 1.26509i 0.291735 + 1.65451i 0 −2.47296 + 0.940471i 0.0549773 + 0.0317412i 0 −2.89829 + 1.67333i
62.19 0.752422 + 2.06726i 0 −2.17534 + 1.82533i −0.562637 − 3.19087i 0 1.24057 + 2.33688i −1.59981 − 0.923650i 0 6.17302 − 3.56400i
62.20 0.752422 + 2.06726i 0 −2.17534 + 1.82533i 0.562637 + 3.19087i 0 2.51680 + 0.815925i −1.59981 − 0.923650i 0 −6.17302 + 3.56400i
See next 80 embeddings (of 132 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 62.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
27.f odd 18 1 inner
189.be even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.2.be.a 132
3.b odd 2 1 189.2.be.a ✓ 132
7.b odd 2 1 inner 567.2.be.a 132
21.c even 2 1 189.2.be.a ✓ 132
27.e even 9 1 189.2.be.a ✓ 132
27.f odd 18 1 inner 567.2.be.a 132
189.y odd 18 1 189.2.be.a ✓ 132
189.be even 18 1 inner 567.2.be.a 132
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
189.2.be.a ✓ 132 3.b odd 2 1
189.2.be.a ✓ 132 21.c even 2 1
189.2.be.a ✓ 132 27.e even 9 1
189.2.be.a ✓ 132 189.y odd 18 1
567.2.be.a 132 1.a even 1 1 trivial
567.2.be.a 132 7.b odd 2 1 inner
567.2.be.a 132 27.f odd 18 1 inner
567.2.be.a 132 189.be even 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(567, [\chi])\).