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Properties

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

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
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 \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29}+ \cdots - 99 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
37.1 −0.475852 − 2.69869i 0 −5.17712 + 1.88432i −0.0114982 + 0.0652096i 0 2.53330 + 0.763145i 4.80842 + 8.32842i 0 0.181452
37.2 −0.442261 − 2.50819i 0 −4.21603 + 1.53451i 0.331479 − 1.87991i 0 0.0136229 − 2.64572i 3.16655 + 5.48462i 0 −4.86178
37.3 −0.379821 − 2.15407i 0 −2.61637 + 0.952279i 0.347563 − 1.97113i 0 0.0877467 + 2.64430i 0.857725 + 1.48562i 0 −4.37795
37.4 −0.351787 − 1.99508i 0 −1.97722 + 0.719650i −0.155052 + 0.879341i 0 −1.72949 + 2.00222i 0.105462 + 0.182666i 0 1.80890
37.5 −0.337831 − 1.91594i 0 −1.67729 + 0.610485i −0.582582 + 3.30399i 0 0.666452 − 2.56044i −0.209199 − 0.362343i 0 6.52704
37.6 −0.306313 − 1.73719i 0 −1.04461 + 0.380207i 0.723302 − 4.10205i 0 −1.55501 − 2.14055i −0.783518 − 1.35709i 0 −7.34759
37.7 −0.278319 − 1.57843i 0 −0.534587 + 0.194574i −0.620906 + 3.52133i 0 −2.64260 + 0.129178i −1.14687 − 1.98644i 0 5.73098
37.8 −0.162199 − 0.919879i 0 1.05952 − 0.385633i 0.120368 − 0.682641i 0 1.39323 − 2.24920i −1.46066 − 2.52993i 0 −0.647471
37.9 −0.161602 − 0.916488i 0 1.06555 − 0.387829i −0.260888 + 1.47957i 0 1.80008 + 1.93899i −1.45826 − 2.52578i 0 1.39817
37.10 −0.0910389 − 0.516307i 0 1.62110 − 0.590032i −0.0290567 + 0.164789i 0 −0.352779 + 2.62213i −0.976493 − 1.69134i 0 0.0877269
37.11 −0.0119703 − 0.0678870i 0 1.87492 − 0.682415i −0.115724 + 0.656302i 0 −1.45670 − 2.20863i −0.137705 − 0.238512i 0 0.0459397
37.12 0.000974390 0.00552604i 0 1.87936 − 0.684030i 0.601605 − 3.41187i 0 2.41288 − 1.08535i 0.0112225 + 0.0194379i 0 0.0194403
37.13 0.0572325 + 0.324581i 0 1.77731 − 0.646887i 0.607976 − 3.44800i 0 −2.50814 + 0.842165i 0.641276 + 1.11072i 0 1.15395
37.14 0.162149 + 0.919594i 0 1.06003 − 0.385818i −0.575026 + 3.26114i 0 1.06445 + 2.42218i 1.46046 + 2.52959i 0 −3.09216
37.15 0.177652 + 1.00751i 0 0.895865 − 0.326068i −0.356801 + 2.02352i 0 −2.48566 + 0.906357i 1.51072 + 2.61665i 0 −2.10210
37.16 0.199381 + 1.13075i 0 0.640547 − 0.233140i 0.0295570 − 0.167626i 0 −1.82867 − 1.91206i 1.53953 + 2.66654i 0 0.195436
37.17 0.202689 + 1.14951i 0 0.599102 − 0.218055i 0.490607 − 2.78237i 0 2.49252 + 0.887321i 1.53933 + 2.66619i 0 3.29779
37.18 0.303930 + 1.72367i 0 −0.999292 + 0.363713i −0.0231991 + 0.131569i 0 1.74352 − 1.99001i 0.819627 + 1.41964i 0 −0.233833
37.19 0.345866 + 1.96151i 0 −1.84850 + 0.672798i −0.424474 + 2.40731i 0 2.63001 + 0.288173i 0.0327363 + 0.0567010i 0 −4.86876
37.20 0.402178 + 2.28086i 0 −3.16120 + 1.15058i −0.125418 + 0.711279i 0 −2.42560 + 1.05663i −1.57964 − 2.73601i 0 −1.67277
See next 80 embeddings (of 132 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 37.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
189.w even 9 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.2.w.a 132
3.b odd 2 1 189.2.w.a yes 132
7.c even 3 1 567.2.u.a 132
21.h odd 6 1 189.2.u.a ✓ 132
27.e even 9 1 567.2.u.a 132
27.f odd 18 1 189.2.u.a ✓ 132
189.w even 9 1 inner 567.2.w.a 132
189.bf odd 18 1 189.2.w.a yes 132
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
189.2.u.a ✓ 132 21.h odd 6 1
189.2.u.a ✓ 132 27.f odd 18 1
189.2.w.a yes 132 3.b odd 2 1
189.2.w.a yes 132 189.bf odd 18 1
567.2.u.a 132 7.c even 3 1
567.2.u.a 132 27.e even 9 1
567.2.w.a 132 1.a even 1 1 trivial
567.2.w.a 132 189.w even 9 1 inner

Hecke kernels

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