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Properties

Label 567.2.bl.a
Level $567$
Weight $2$
Character orbit 567.bl
Analytic conductor $4.528$
Analytic rank $0$
Dimension $1260$
CM no
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(47,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([7, 45]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.bl (of order \(54\), degree \(18\), 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: \(1260\)
Relative dimension: \(70\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9} - 27 q^{10} - 9 q^{11} - 27 q^{12} - 18 q^{14} - 36 q^{15} - 9 q^{16} - 27 q^{17} - 9 q^{18} - 27 q^{19} + 9 q^{21} - 36 q^{22} + 18 q^{23} - 27 q^{24} - 9 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 117 q^{30} - 27 q^{31} - 9 q^{32} - 27 q^{33} - 72 q^{35} - 36 q^{36} - 9 q^{37} - 27 q^{38} - 9 q^{39} - 27 q^{40} - 54 q^{41} - 63 q^{42} - 36 q^{43} - 9 q^{44} - 27 q^{45} - 9 q^{46} - 27 q^{47} + 297 q^{48} - 18 q^{49} - 36 q^{50} - 9 q^{51} - 27 q^{52} - 27 q^{53} - 405 q^{54} + 198 q^{56} - 36 q^{57} - 9 q^{58} - 27 q^{59} - 9 q^{60} - 27 q^{61} - 297 q^{62} - 72 q^{63} - 36 q^{64} - 27 q^{65} - 27 q^{66} - 9 q^{67} - 27 q^{68} + 54 q^{69} - 126 q^{70} + 36 q^{71} - 117 q^{72} - 27 q^{73} - 9 q^{74} - 27 q^{75} + 54 q^{77} + 81 q^{78} + 99 q^{79} - 9 q^{81} - 54 q^{82} + 81 q^{84} - 90 q^{85} - 81 q^{86} - 27 q^{87} - 9 q^{88} - 27 q^{89} - 18 q^{91} + 90 q^{92} - 45 q^{93} - 27 q^{94} - 225 q^{95} - 27 q^{96} + 360 q^{98} - 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
47.1 −2.25981 + 1.68236i 1.33718 − 1.10088i 1.70277 − 5.68766i −1.03032 − 0.517444i −1.16969 + 4.73741i 2.49750 − 0.873223i 3.79364 + 10.4229i 0.576122 − 2.94416i 3.19884 − 0.564042i
47.2 −2.15784 + 1.60645i 1.04035 + 1.38480i 1.50198 − 5.01695i 0.816686 + 0.410155i −4.46952 − 1.31691i −1.84565 + 1.89567i 2.97828 + 8.18277i −0.835352 + 2.88135i −2.42117 + 0.426918i
47.3 −2.07222 + 1.54271i −0.633121 − 1.61219i 1.34053 − 4.47769i −2.63074 − 1.32121i 3.79911 + 2.36409i −2.37831 + 1.15916i 2.36274 + 6.49157i −2.19831 + 2.04142i 7.48970 − 1.32064i
47.4 −2.04476 + 1.52227i −0.925700 + 1.46393i 1.29015 − 4.30939i 3.11099 + 1.56240i −0.335655 − 4.40255i 0.240867 − 2.63476i 2.17826 + 5.98472i −1.28616 − 2.71031i −8.73964 + 1.54103i
47.5 −2.01627 + 1.50106i −1.58212 + 0.704907i 1.23857 − 4.13711i −2.56014 − 1.28575i 2.13188 − 3.79614i 2.12163 + 1.58073i 1.99330 + 5.47655i 2.00621 − 2.23050i 7.09191 − 1.25050i
47.6 −2.00728 + 1.49437i −1.62798 − 0.591336i 1.22245 − 4.08327i 2.80443 + 1.40844i 4.15149 − 1.24582i 2.06408 + 1.65516i 1.93631 + 5.31997i 2.30064 + 1.92537i −7.73400 + 1.36371i
47.7 −1.95911 + 1.45850i 0.633276 + 1.61213i 1.13727 − 3.79875i −1.19116 − 0.598225i −3.59195 − 2.23470i 2.03468 − 1.69118i 1.64174 + 4.51065i −2.19792 + 2.04184i 3.20613 − 0.565327i
47.8 −1.90357 + 1.41715i −0.580000 − 1.63205i 1.04164 − 3.47932i 1.19955 + 0.602435i 3.41694 + 2.28478i −0.514394 − 2.59526i 1.32456 + 3.63920i −2.32720 + 1.89318i −3.13716 + 0.553166i
47.9 −1.85105 + 1.37806i 1.73009 − 0.0823391i 0.953742 − 3.18572i 0.0699628 + 0.0351366i −3.08902 + 2.53658i −1.86228 − 1.87934i 1.04612 + 2.87420i 2.98644 − 0.284909i −0.177925 + 0.0313729i
47.10 −1.82471 + 1.35845i −0.0367015 − 1.73166i 0.910585 − 3.04157i 1.22141 + 0.613415i 2.41934 + 3.10993i 1.94865 + 1.78963i 0.914162 + 2.51164i −2.99731 + 0.127109i −3.06201 + 0.539915i
47.11 −1.68096 + 1.25143i −0.880483 + 1.49156i 0.685953 − 2.29124i 1.14042 + 0.572741i −0.386525 − 3.60912i −0.739432 + 2.54032i 0.280765 + 0.771395i −1.44950 − 2.62658i −2.63375 + 0.464401i
47.12 −1.60846 + 1.19745i 1.72593 − 0.145494i 0.579642 − 1.93614i 1.42068 + 0.713495i −2.60187 + 2.30074i 0.382623 + 2.61794i 0.0144340 + 0.0396572i 2.95766 − 0.502224i −3.13949 + 0.553577i
47.13 −1.60165 + 1.19238i −1.67040 − 0.458005i 0.569890 − 1.90357i −1.73578 − 0.871741i 3.22150 − 1.25819i 0.506740 − 2.59677i −0.00884881 − 0.0243119i 2.58046 + 1.53010i 3.81955 − 0.673490i
47.14 −1.52016 + 1.13172i 1.19475 − 1.25403i 0.456502 − 1.52482i −2.69581 − 1.35389i −0.397006 + 3.25844i −2.49268 − 0.886878i −0.264662 − 0.727154i −0.145158 − 2.99649i 5.63029 − 0.992772i
47.15 −1.51918 + 1.13099i 1.63369 + 0.575362i 0.455174 − 1.52039i −3.43280 − 1.72402i −3.13261 + 0.973612i 2.16641 + 1.51877i −0.267490 − 0.734924i 2.33792 + 1.87993i 7.16491 − 1.26337i
47.16 −1.48796 + 1.10775i 0.0624177 + 1.73093i 0.413321 − 1.38059i −3.16479 − 1.58942i −2.01030 − 2.50641i −2.48697 + 0.902769i −0.354579 − 0.974199i −2.99221 + 0.216081i 6.46975 − 1.14079i
47.17 −1.35313 + 1.00737i 1.30075 + 1.14371i 0.242564 − 0.810220i 3.29454 + 1.65458i −2.91221 − 0.237253i −0.960966 − 2.46506i −0.665963 − 1.82972i 0.383877 + 2.97534i −6.12472 + 1.07995i
47.18 −1.27812 + 0.951523i −1.38984 − 1.03360i 0.154581 − 0.516338i 3.17606 + 1.59508i 2.75988 − 0.00139844i −2.56129 + 0.663185i −0.796228 − 2.18762i 0.863322 + 2.87310i −5.57714 + 0.983400i
47.19 −1.27799 + 0.951428i −1.56326 + 0.745807i 0.154436 − 0.515851i 0.0768138 + 0.0385773i 1.28824 − 2.44046i −2.56617 − 0.644028i −0.796425 − 2.18816i 1.88754 − 2.33177i −0.134871 + 0.0237814i
47.20 −1.22394 + 0.911190i 1.29436 − 1.15093i 0.0941575 − 0.314508i 2.46339 + 1.23716i −0.535500 + 2.58808i 2.26450 − 1.36822i −0.872428 − 2.39698i 0.350720 − 2.97943i −4.14233 + 0.730405i
See next 80 embeddings (of 1260 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 47.70
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
567.bl even 54 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.2.bl.a ✓ 1260
7.d odd 6 1 567.2.br.a yes 1260
81.h odd 54 1 567.2.br.a yes 1260
567.bl even 54 1 inner 567.2.bl.a ✓ 1260
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
567.2.bl.a ✓ 1260 1.a even 1 1 trivial
567.2.bl.a ✓ 1260 567.bl even 54 1 inner
567.2.br.a yes 1260 7.d odd 6 1
567.2.br.a yes 1260 81.h odd 54 1

Hecke kernels

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