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Properties

Label 890.2.o.a
Level $890$
Weight $2$
Character orbit 890.o
Analytic conductor $7.107$
Analytic rank $0$
Dimension $60$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [890,2,Mod(91,890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(890, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("890.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 890 = 2 \cdot 5 \cdot 89 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 890.o (of order \(11\), degree \(10\), 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: \(7.10668577989\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} - 30 q^{13} + 6 q^{14} + 4 q^{15} - 6 q^{16} - 10 q^{17} + 6 q^{18} + 7 q^{19} - 6 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
91.1 −0.959493 + 0.281733i −2.15610 − 1.38564i 0.841254 − 0.540641i −0.654861 + 0.755750i 2.45914 + 0.722068i −2.60674 + 3.00834i −0.654861 + 0.755750i 1.48251 + 3.24625i 0.415415 − 0.909632i
91.2 −0.959493 + 0.281733i −0.970228 − 0.623528i 0.841254 − 0.540641i −0.654861 + 0.755750i 1.10660 + 0.324926i 1.95889 − 2.26068i −0.654861 + 0.755750i −0.693689 − 1.51897i 0.415415 − 0.909632i
91.3 −0.959493 + 0.281733i −0.0785546 − 0.0504840i 0.841254 − 0.540641i −0.654861 + 0.755750i 0.0895956 + 0.0263076i −0.739256 + 0.853147i −0.654861 + 0.755750i −1.24262 − 2.72096i 0.415415 − 0.909632i
91.4 −0.959493 + 0.281733i 1.09596 + 0.704333i 0.841254 − 0.540641i −0.654861 + 0.755750i −1.25000 − 0.367034i 0.906125 − 1.04572i −0.654861 + 0.755750i −0.541194 − 1.18505i 0.415415 − 0.909632i
91.5 −0.959493 + 0.281733i 1.18519 + 0.761672i 0.841254 − 0.540641i −0.654861 + 0.755750i −1.35177 − 0.396914i −0.694605 + 0.801617i −0.654861 + 0.755750i −0.421725 − 0.923450i 0.415415 − 0.909632i
91.6 −0.959493 + 0.281733i 2.26498 + 1.45562i 0.841254 − 0.540641i −0.654861 + 0.755750i −2.58333 − 0.758534i −0.453862 + 0.523785i −0.654861 + 0.755750i 1.76509 + 3.86500i 0.415415 − 0.909632i
121.1 −0.142315 + 0.989821i −2.59272 + 0.761291i −0.959493 − 0.281733i 0.415415 − 0.909632i −0.384560 − 2.67467i −1.47545 + 3.23078i 0.415415 − 0.909632i 3.61886 − 2.32570i 0.841254 + 0.540641i
121.2 −0.142315 + 0.989821i −2.13119 + 0.625774i −0.959493 − 0.281733i 0.415415 − 0.909632i −0.316104 − 2.19855i 1.98779 − 4.35266i 0.415415 − 0.909632i 1.62662 − 1.04536i 0.841254 + 0.540641i
121.3 −0.142315 + 0.989821i −0.724740 + 0.212803i −0.959493 − 0.281733i 0.415415 − 0.909632i −0.107496 − 0.747649i −0.0604032 + 0.132265i 0.415415 − 0.909632i −2.04380 + 1.31347i 0.841254 + 0.540641i
121.4 −0.142315 + 0.989821i 0.707712 − 0.207803i −0.959493 − 0.281733i 0.415415 − 0.909632i 0.104970 + 0.730082i 1.04299 − 2.28383i 0.415415 − 0.909632i −2.06609 + 1.32779i 0.841254 + 0.540641i
121.5 −0.142315 + 0.989821i 1.15127 − 0.338042i −0.959493 − 0.281733i 0.415415 − 0.909632i 0.170759 + 1.18766i −0.834221 + 1.82669i 0.415415 − 0.909632i −1.31262 + 0.843570i 0.841254 + 0.540641i
121.6 −0.142315 + 0.989821i 3.13018 − 0.919103i −0.959493 − 0.281733i 0.415415 − 0.909632i 0.464277 + 3.22912i 0.545687 − 1.19489i 0.415415 − 0.909632i 6.42950 − 4.13199i 0.841254 + 0.540641i
271.1 0.841254 − 0.540641i −0.881612 − 1.93046i 0.415415 − 0.909632i −0.142315 − 0.989821i −1.78534 − 1.14737i −0.00872159 − 0.0606600i −0.142315 − 0.989821i −0.984857 + 1.13659i −0.654861 − 0.755750i
271.2 0.841254 − 0.540641i −0.608481 − 1.33239i 0.415415 − 0.909632i −0.142315 − 0.989821i −1.23223 − 0.791906i −0.345110 − 2.40030i −0.142315 − 0.989821i 0.559573 − 0.645782i −0.654861 − 0.755750i
271.3 0.841254 − 0.540641i 0.249407 + 0.546126i 0.415415 − 0.909632i −0.142315 − 0.989821i 0.505073 + 0.324591i −0.576031 − 4.00638i −0.142315 − 0.989821i 1.72853 − 1.99483i −0.654861 − 0.755750i
271.4 0.841254 − 0.540641i 0.312407 + 0.684075i 0.415415 − 0.909632i −0.142315 − 0.989821i 0.632652 + 0.406581i 0.110561 + 0.768972i −0.142315 − 0.989821i 1.59422 − 1.83983i −0.654861 − 0.755750i
271.5 0.841254 − 0.540641i 0.606764 + 1.32863i 0.415415 − 0.909632i −0.142315 − 0.989821i 1.22875 + 0.789671i 0.0430450 + 0.299384i −0.142315 − 0.989821i 0.567494 − 0.654923i −0.654861 − 0.755750i
271.6 0.841254 − 0.540641i 1.23693 + 2.70850i 0.415415 − 0.909632i −0.142315 − 0.989821i 2.50490 + 1.60980i 0.469502 + 3.26546i −0.142315 − 0.989821i −3.84139 + 4.43320i −0.654861 − 0.755750i
331.1 −0.142315 − 0.989821i −2.59272 − 0.761291i −0.959493 + 0.281733i 0.415415 + 0.909632i −0.384560 + 2.67467i −1.47545 − 3.23078i 0.415415 + 0.909632i 3.61886 + 2.32570i 0.841254 − 0.540641i
331.2 −0.142315 − 0.989821i −2.13119 − 0.625774i −0.959493 + 0.281733i 0.415415 + 0.909632i −0.316104 + 2.19855i 1.98779 + 4.35266i 0.415415 + 0.909632i 1.62662 + 1.04536i 0.841254 − 0.540641i
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 91.6
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
89.e even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 890.2.o.a ✓ 60
89.e even 11 1 inner 890.2.o.a ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
890.2.o.a ✓ 60 1.a even 1 1 trivial
890.2.o.a ✓ 60 89.e even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{60} - 4 T_{3}^{59} + 14 T_{3}^{58} - 25 T_{3}^{57} + 47 T_{3}^{56} - 204 T_{3}^{55} + \cdots + 543169 \) acting on \(S_{2}^{\mathrm{new}}(890, [\chi])\). Copy content Toggle raw display