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Properties

Label 927.2.u.d
Level $927$
Weight $2$
Character orbit 927.u
Analytic conductor $7.402$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [927,2,Mod(64,927)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(927, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([0, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("927.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 927.u (of order \(17\), degree \(16\), 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: \(7.40213226737\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{17})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{17}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 288 q - 20 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 288 q - 20 q^{4} - 8 q^{7} + 72 q^{10} - 8 q^{13} - 32 q^{16} - 34 q^{19} - 28 q^{22} + 22 q^{25} + 88 q^{28} + 16 q^{31} + 110 q^{34} - 16 q^{37} + 28 q^{40} - 32 q^{43} - 176 q^{46} - 82 q^{49} - 32 q^{55} + 68 q^{58} - 24 q^{61} + 54 q^{64} + 28 q^{67} + 44 q^{70} + 48 q^{73} - 242 q^{82} + 18 q^{85} + 214 q^{88} + 114 q^{91} + 108 q^{94} + 196 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −2.47704 + 0.959610i 0 3.73685 − 3.40659i 0.201799 − 0.709248i 0 −2.09555 − 4.20842i −3.61919 + 7.26832i 0 0.180739 + 1.95048i
64.2 −2.39557 + 0.928048i 0 3.39945 − 3.09901i −0.651650 + 2.29031i 0 1.50615 + 3.02477i −2.97734 + 5.97930i 0 −0.564447 − 6.09135i
64.3 −2.01317 + 0.779904i 0 1.96657 − 1.79276i 0.659243 − 2.31700i 0 1.02960 + 2.06773i −0.636182 + 1.27762i 0 0.479873 + 5.17865i
64.4 −1.89024 + 0.732284i 0 1.55876 − 1.42100i −1.19656 + 4.20547i 0 −0.922655 − 1.85294i −0.0987260 + 0.198269i 0 −0.817811 − 8.82558i
64.5 −1.58164 + 0.612730i 0 0.648123 − 0.590842i 0.214160 − 0.752694i 0 0.327349 + 0.657405i 0.849033 − 1.70509i 0 0.122475 + 1.32171i
64.6 −1.11205 + 0.430811i 0 −0.426958 + 0.389223i 0.774227 − 2.72112i 0 −1.74382 − 3.50205i 1.37028 − 2.75189i 0 0.311310 + 3.35958i
64.7 −0.733841 + 0.284292i 0 −1.02032 + 0.930141i −0.326205 + 1.14649i 0 1.77404 + 3.56276i 1.18590 − 2.38160i 0 −0.0865552 − 0.934080i
64.8 −0.638851 + 0.247492i 0 −1.13114 + 1.03117i −0.611516 + 2.14926i 0 −0.0403670 − 0.0810678i 1.07819 − 2.16529i 0 −0.141256 − 1.52440i
64.9 −0.401142 + 0.155403i 0 −1.34125 + 1.22271i −0.474209 + 1.66667i 0 −1.24830 − 2.50692i 0.731525 − 1.46910i 0 −0.0687810 − 0.742265i
64.10 0.401142 − 0.155403i 0 −1.34125 + 1.22271i 0.474209 − 1.66667i 0 −1.24830 − 2.50692i −0.731525 + 1.46910i 0 −0.0687810 − 0.742265i
64.11 0.638851 − 0.247492i 0 −1.13114 + 1.03117i 0.611516 − 2.14926i 0 −0.0403670 − 0.0810678i −1.07819 + 2.16529i 0 −0.141256 − 1.52440i
64.12 0.733841 − 0.284292i 0 −1.02032 + 0.930141i 0.326205 − 1.14649i 0 1.77404 + 3.56276i −1.18590 + 2.38160i 0 −0.0865552 − 0.934080i
64.13 1.11205 − 0.430811i 0 −0.426958 + 0.389223i −0.774227 + 2.72112i 0 −1.74382 − 3.50205i −1.37028 + 2.75189i 0 0.311310 + 3.35958i
64.14 1.58164 − 0.612730i 0 0.648123 − 0.590842i −0.214160 + 0.752694i 0 0.327349 + 0.657405i −0.849033 + 1.70509i 0 0.122475 + 1.32171i
64.15 1.89024 − 0.732284i 0 1.55876 − 1.42100i 1.19656 − 4.20547i 0 −0.922655 − 1.85294i 0.0987260 − 0.198269i 0 −0.817811 − 8.82558i
64.16 2.01317 − 0.779904i 0 1.96657 − 1.79276i −0.659243 + 2.31700i 0 1.02960 + 2.06773i 0.636182 − 1.27762i 0 0.479873 + 5.17865i
64.17 2.39557 − 0.928048i 0 3.39945 − 3.09901i 0.651650 − 2.29031i 0 1.50615 + 3.02477i 2.97734 − 5.97930i 0 −0.564447 − 6.09135i
64.18 2.47704 − 0.959610i 0 3.73685 − 3.40659i −0.201799 + 0.709248i 0 −2.09555 − 4.20842i 3.61919 − 7.26832i 0 0.180739 + 1.95048i
100.1 −2.36545 + 1.46463i 0 2.55876 − 5.13869i −1.94687 + 0.754220i 0 −0.459752 + 4.96151i 0.960213 + 10.3623i 0 3.50057 − 4.63550i
100.2 −2.03126 + 1.25770i 0 1.65271 − 3.31909i −1.79209 + 0.694260i 0 0.367270 − 3.96347i 0.376466 + 4.06272i 0 2.76702 − 3.66413i
See next 80 embeddings (of 288 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 64.18
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
103.e even 17 1 inner
309.l odd 34 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 927.2.u.d ✓ 288
3.b odd 2 1 inner 927.2.u.d ✓ 288
103.e even 17 1 inner 927.2.u.d ✓ 288
309.l odd 34 1 inner 927.2.u.d ✓ 288
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
927.2.u.d ✓ 288 1.a even 1 1 trivial
927.2.u.d ✓ 288 3.b odd 2 1 inner
927.2.u.d ✓ 288 103.e even 17 1 inner
927.2.u.d ✓ 288 309.l odd 34 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{288} + 28 T_{2}^{286} + 466 T_{2}^{284} + 6015 T_{2}^{282} + 66795 T_{2}^{280} + \cdots + 12\!\cdots\!81 \) acting on \(S_{2}^{\mathrm{new}}(927, [\chi])\). Copy content Toggle raw display