Properties

Label 891.2.j.c
Level $891$
Weight $2$
Character orbit 891.j
Analytic conductor $7.115$
Analytic rank $0$
Dimension $102$
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] = [891,2,Mod(100,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.j (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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(102\)
Relative dimension: \(17\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 297)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 102 q + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 102 q + 6 q^{5} - 18 q^{10} + 21 q^{14} - 30 q^{19} - 27 q^{20} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 72 q^{28} + 18 q^{29} - 12 q^{31} - 96 q^{32} - 24 q^{34} - 9 q^{35} - 48 q^{37} + 15 q^{38} + 90 q^{40} + 30 q^{43} + 60 q^{44} - 42 q^{46} + 30 q^{47} - 36 q^{49} - 66 q^{50} - 84 q^{52} - 36 q^{53} + 12 q^{55} + 48 q^{56} - 75 q^{58} + 42 q^{59} - 42 q^{61} - 114 q^{64} + 57 q^{65} + 54 q^{67} + 6 q^{68} + 204 q^{70} + 30 q^{71} - 69 q^{73} + 117 q^{74} - 60 q^{76} - 18 q^{79} - 84 q^{80} + 84 q^{82} + 6 q^{83} - 39 q^{85} + 132 q^{86} - 9 q^{88} + 15 q^{89} - 69 q^{91} - 102 q^{92} + 123 q^{94} - 66 q^{95} + 66 q^{97} - 57 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
100.1 −2.49990 + 0.909890i 0 3.88953 3.26370i −0.522073 2.96082i 0 −3.45741 2.90111i −4.09349 + 7.09013i 0 3.99915 + 6.92674i
100.2 −2.34369 + 0.853033i 0 3.23312 2.71291i 0.146799 + 0.832538i 0 2.11009 + 1.77058i −2.76913 + 4.79628i 0 −1.05423 1.82599i
100.3 −2.16807 + 0.789111i 0 2.54572 2.13611i 0.640629 + 3.63319i 0 2.09099 + 1.75455i −1.52645 + 2.64389i 0 −4.25591 7.37146i
100.4 −1.72658 + 0.628423i 0 1.05407 0.884470i −0.647122 3.67001i 0 0.682898 + 0.573019i 0.573273 0.992939i 0 3.42363 + 5.92989i
100.5 −1.54616 + 0.562758i 0 0.541838 0.454656i 0.309482 + 1.75516i 0 −1.57643 1.32278i 1.06348 1.84201i 0 −1.46624 2.53960i
100.6 −1.01578 + 0.369713i 0 −0.636972 + 0.534483i 0.488157 + 2.76848i 0 −1.61165 1.35233i 1.53038 2.65070i 0 −1.51940 2.63168i
100.7 −0.877023 + 0.319210i 0 −0.864815 + 0.725666i −0.342989 1.94519i 0 3.86422 + 3.24246i 1.46013 2.52902i 0 0.921732 + 1.59649i
100.8 −0.355283 + 0.129312i 0 −1.42258 + 1.19369i −0.186000 1.05486i 0 −3.05909 2.56688i 0.729146 1.26292i 0 0.202489 + 0.350721i
100.9 −0.172647 + 0.0628383i 0 −1.50623 + 1.26388i −0.119032 0.675063i 0 0.656550 + 0.550911i 0.364353 0.631077i 0 0.0629702 + 0.109068i
100.10 0.583438 0.212354i 0 −1.23678 + 1.03778i −0.0810529 0.459674i 0 −2.02973 1.70315i −1.12209 + 1.94352i 0 −0.144903 0.250979i
100.11 0.949421 0.345561i 0 −0.750101 + 0.629409i 0.529508 + 3.00299i 0 0.254047 + 0.213171i −1.50502 + 2.60676i 0 1.54044 + 2.66812i
100.12 1.18215 0.430266i 0 −0.319750 + 0.268302i −0.736637 4.17768i 0 −1.09698 0.920474i −1.52056 + 2.63369i 0 −2.66832 4.62167i
100.13 1.20959 0.440255i 0 −0.262804 + 0.220519i −0.0689078 0.390796i 0 −0.0154059 0.0129271i −1.50802 + 2.61197i 0 −0.255400 0.442366i
100.14 1.60221 0.583158i 0 0.694922 0.583109i −0.151385 0.858546i 0 3.87388 + 3.25057i −0.931670 + 1.61370i 0 −0.743218 1.28729i
100.15 2.27218 0.827005i 0 2.94677 2.47263i −0.646856 3.66851i 0 1.11607 + 0.936496i 2.23270 3.86715i 0 −4.50365 7.80054i
100.16 2.30441 0.838737i 0 3.07474 2.58002i 0.647325 + 3.67116i 0 1.74400 + 1.46339i 2.46922 4.27681i 0 4.57085 + 7.91694i
100.17 2.60173 0.946954i 0 4.34021 3.64187i −0.139232 0.789623i 0 −0.481874 0.404340i 5.07469 8.78962i 0 −1.10998 1.92254i
199.1 −2.00483 + 1.68225i 0 0.842077 4.77565i 2.77519 1.01009i 0 0.582954 + 3.30610i 3.72852 + 6.45798i 0 −3.86457 + 6.69363i
199.2 −1.89627 + 1.59116i 0 0.716758 4.06494i −0.590212 + 0.214820i 0 0.209925 + 1.19055i 2.63339 + 4.56117i 0 0.777390 1.34648i
199.3 −1.64996 + 1.38448i 0 0.458281 2.59904i 3.14380 1.14425i 0 −0.832538 4.72156i 0.688308 + 1.19218i 0 −3.60295 + 6.24049i
See next 80 embeddings (of 102 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 100.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
27.e even 9 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 891.2.j.c 102
3.b odd 2 1 297.2.j.c 102
27.e even 9 1 inner 891.2.j.c 102
27.e even 9 1 8019.2.a.k 51
27.f odd 18 1 297.2.j.c 102
27.f odd 18 1 8019.2.a.l 51
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
297.2.j.c 102 3.b odd 2 1
297.2.j.c 102 27.f odd 18 1
891.2.j.c 102 1.a even 1 1 trivial
891.2.j.c 102 27.e even 9 1 inner
8019.2.a.k 51 27.e even 9 1
8019.2.a.l 51 27.f odd 18 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{102} + 48 T_{2}^{97} + 849 T_{2}^{96} - 78 T_{2}^{95} - 42 T_{2}^{94} - 506 T_{2}^{93} + 543 T_{2}^{92} + 37908 T_{2}^{91} + 482382 T_{2}^{90} + 55125 T_{2}^{89} + 64287 T_{2}^{88} - 320637 T_{2}^{87} - 155952 T_{2}^{86} + \cdots + 331776 \) acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\). Copy content Toggle raw display