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Properties

Label 567.2.bh.a
Level $567$
Weight $2$
Character orbit 567.bh
Analytic conductor $4.528$
Analytic rank $0$
Dimension $486$
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(22,567)]
 
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([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.bh (of order \(27\), 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: \(486\)
Relative dimension: \(27\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 486 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 486 q - 126 q^{12} - 9 q^{18} - 36 q^{20} - 54 q^{24} + 54 q^{25} + 54 q^{26} + 63 q^{27} + 243 q^{28} - 27 q^{29} - 54 q^{32} - 36 q^{36} - 207 q^{38} + 36 q^{39} - 54 q^{41} - 72 q^{44} - 54 q^{45} - 117 q^{50} - 207 q^{51} + 90 q^{53} - 216 q^{54} - 54 q^{57} - 63 q^{59} - 117 q^{60} + 36 q^{65} + 153 q^{66} - 135 q^{67} + 270 q^{68} + 99 q^{69} + 36 q^{71} + 108 q^{72} + 144 q^{74} + 90 q^{75} - 81 q^{76} - 18 q^{77} + 162 q^{78} - 27 q^{79} - 396 q^{80} + 144 q^{81} - 108 q^{83} - 27 q^{85} + 72 q^{86} - 81 q^{88} + 63 q^{89} - 9 q^{90} + 306 q^{92} - 162 q^{93} + 180 q^{95} - 279 q^{96} - 27 q^{97} + 18 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −1.92835 − 2.04393i −1.59215 + 0.681942i −0.342832 + 5.88620i 1.11733 − 0.130597i 4.46407 + 1.93923i −0.893633 − 0.448799i 8.38689 − 7.03744i 2.06991 − 2.17151i −2.42154 − 2.03191i
22.2 −1.65038 − 1.74930i 1.12036 − 1.32091i −0.220008 + 3.77740i −0.119222 + 0.0139351i −4.15968 + 0.220161i −0.893633 − 0.448799i 3.28630 − 2.75753i −0.489601 − 2.95978i 0.221139 + 0.185558i
22.3 −1.54979 − 1.64268i −0.0709154 + 1.73060i −0.180263 + 3.09500i −3.02949 + 0.354097i 2.95272 − 2.56557i −0.893633 − 0.448799i 1.90344 − 1.59717i −2.98994 − 0.245452i 5.27674 + 4.42771i
22.4 −1.45566 − 1.54290i −0.584666 − 1.63039i −0.145332 + 2.49526i 1.76835 − 0.206691i −1.66446 + 3.27537i −0.893633 − 0.448799i 0.811634 − 0.681042i −2.31633 + 1.90646i −2.89302 − 2.42753i
22.5 −1.41570 − 1.50056i 1.72610 − 0.143406i −0.131168 + 2.25208i −2.02404 + 0.236577i −2.65884 − 2.38710i −0.893633 − 0.448799i 0.404396 − 0.339328i 2.95887 − 0.495066i 3.22044 + 2.70227i
22.6 −1.29699 − 1.37473i −1.64868 − 0.530898i −0.0914062 + 1.56938i 2.78814 − 0.325887i 1.40848 + 2.95505i −0.893633 − 0.448799i −0.619601 + 0.519907i 2.43629 + 1.75056i −4.06419 − 3.41026i
22.7 −1.03321 − 1.09514i −1.19395 + 1.25479i −0.0155172 + 0.266421i 0.781815 − 0.0913810i 2.60778 + 0.0110798i −0.893633 − 0.448799i −1.99893 + 1.67730i −0.148979 − 2.99630i −0.907858 − 0.761783i
22.8 −0.983359 − 1.04230i 1.72136 + 0.192140i −0.00310409 + 0.0532952i 3.80159 − 0.444343i −1.49245 − 1.98312i −0.893633 − 0.448799i −2.13683 + 1.79301i 2.92616 + 0.661485i −4.20147 − 3.52545i
22.9 −0.767931 − 0.813960i −0.751082 − 1.56073i 0.0434779 − 0.746486i −3.03708 + 0.354984i −0.693591 + 1.80988i −0.893633 − 0.448799i −2.35547 + 1.97647i −1.87175 + 2.34447i 2.62122 + 2.19946i
22.10 −0.559140 − 0.592654i 0.589158 + 1.62877i 0.0776887 − 1.33386i 2.81565 − 0.329102i 0.635875 − 1.25988i −0.893633 − 0.448799i −2.08228 + 1.74724i −2.30578 + 1.91921i −1.76939 − 1.48469i
22.11 −0.482358 − 0.511269i 0.835237 − 1.51736i 0.0875623 − 1.50339i 0.138933 − 0.0162389i −1.17866 + 0.304879i −0.893633 − 0.448799i −1.88777 + 1.58403i −1.60476 − 2.53471i −0.0753179 − 0.0631992i
22.12 −0.427287 − 0.452897i 1.40801 + 1.00871i 0.0937475 − 1.60958i −3.22168 + 0.376560i −0.144783 − 1.06869i −0.893633 − 0.448799i −1.72298 + 1.44576i 0.965005 + 2.84056i 1.54712 + 1.29819i
22.13 −0.203463 − 0.215658i −1.54340 + 0.786085i 0.111178 − 1.90886i −3.83282 + 0.447993i 0.483550 + 0.172907i −0.893633 − 0.448799i −0.888530 + 0.745565i 1.76414 − 2.42648i 0.876452 + 0.735430i
22.14 −0.0469393 − 0.0497528i −0.277164 + 1.70973i 0.116018 − 1.99195i 0.701656 − 0.0820119i 0.0980738 − 0.0664640i −0.893633 − 0.448799i −0.209346 + 0.175663i −2.84636 − 0.947751i −0.0370156 − 0.0310598i
22.15 0.208221 + 0.220702i −1.68831 − 0.386810i 0.110937 − 1.90471i 0.546664 − 0.0638958i −0.266172 − 0.453154i −0.893633 − 0.448799i 0.908342 − 0.762189i 2.70076 + 1.30611i 0.127929 + 0.107345i
22.16 0.243993 + 0.258618i 0.200864 − 1.72036i 0.108939 − 1.87041i 3.36466 − 0.393273i 0.493926 − 0.367810i −0.893633 − 0.448799i 1.05504 − 0.885281i −2.91931 − 0.691120i 0.922663 + 0.774206i
22.17 0.449367 + 0.476301i 1.72005 − 0.203546i 0.0913575 − 1.56855i −1.30365 + 0.152374i 0.869882 + 0.727794i −0.893633 − 0.448799i 1.79140 − 1.50316i 2.91714 − 0.700220i −0.658391 − 0.552456i
22.18 0.674143 + 0.714549i −1.48586 − 0.890064i 0.0601770 − 1.03320i −1.72566 + 0.201700i −0.365688 − 1.66175i −0.893633 − 0.448799i 2.28392 − 1.91643i 1.41557 + 2.64503i −1.30746 − 1.09709i
22.19 0.979999 + 1.03874i −1.44278 + 0.958328i −0.00228948 + 0.0393089i 0.783557 − 0.0915847i −2.40937 − 0.559507i −0.893633 − 0.448799i 2.14485 − 1.79974i 1.16321 − 2.76531i 0.863018 + 0.724158i
22.20 1.18674 + 1.25787i 0.170232 − 1.72366i −0.0575982 + 0.988922i −2.87982 + 0.336603i 2.37017 − 1.83141i −0.893633 − 0.448799i 1.33720 − 1.12205i −2.94204 − 0.586847i −3.84101 − 3.22299i
See next 80 embeddings (of 486 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 22.27
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
81.g even 27 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 567.2.bh.a ✓ 486
81.g even 27 1 inner 567.2.bh.a ✓ 486
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
567.2.bh.a ✓ 486 1.a even 1 1 trivial
567.2.bh.a ✓ 486 81.g even 27 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{486} + 54 T_{2}^{481} + 99 T_{2}^{479} - 324 T_{2}^{478} - 2851 T_{2}^{477} + \cdots + 10\!\cdots\!01 \) acting on \(S_{2}^{\mathrm{new}}(567, [\chi])\). Copy content Toggle raw display