↑

Properties

Label 55.4.g.b
Level $55$
Weight $4$
Character orbit 55.g
Analytic conductor $3.245$
Analytic rank $0$
Dimension $24$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,4,Mod(16,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 55.g (of order \(5\), degree \(4\), 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: \(3.24510505032\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{2} + 4 q^{3} - 36 q^{4} - 30 q^{5} + 30 q^{6} + 81 q^{7} - 10 q^{8} - 48 q^{9} - 70 q^{10} - 72 q^{11} + 10 q^{12} + 65 q^{13} - 47 q^{14} + 20 q^{15} - 60 q^{16} - 142 q^{17} + 283 q^{18} - 17 q^{19}+ \cdots + 5980 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
16.1 −1.43124 − 4.40490i 6.70801 + 4.87365i −10.8826 + 7.90666i 1.54508 − 4.75528i 11.8672 − 36.5235i 24.3122 − 17.6639i 20.4274 + 14.8414i 12.9014 + 39.7065i −23.1579
16.2 −1.41210 − 4.34600i −5.83785 − 4.24145i −10.4216 + 7.57173i 1.54508 − 4.75528i −10.1897 + 31.3607i 6.50661 − 4.72733i 18.0477 + 13.1124i 7.74716 + 23.8433i −22.8483
16.3 −0.513572 − 1.58061i −1.60233 − 1.16416i 4.23755 − 3.07876i 1.54508 − 4.75528i −1.01717 + 3.13054i −7.13418 + 5.18329i −17.7990 − 12.9317i −7.13127 − 21.9478i −8.30978
16.4 0.267133 + 0.822150i 4.45886 + 3.23955i 5.86756 − 4.26304i 1.54508 − 4.75528i −1.47229 + 4.53124i −2.26519 + 1.64576i 10.6672 + 7.75016i 1.04327 + 3.21086i 4.32230
16.5 0.849844 + 2.61555i −5.86409 − 4.26051i 0.353259 − 0.256657i 1.54508 − 4.75528i 6.16003 − 18.9586i 24.9835 − 18.1516i 18.7709 + 13.6378i 7.89215 + 24.2895i 13.7508
16.6 1.50387 + 4.62843i 4.25544 + 3.09176i −12.6886 + 9.21884i 1.54508 − 4.75528i −7.91037 + 24.3456i 4.59294 − 3.33697i −30.2534 − 21.9804i 0.206327 + 0.635008i 24.3331
26.1 −2.96806 − 2.15642i −0.538187 + 1.65637i 1.68708 + 5.19231i −4.04508 + 2.93893i 5.16920 − 3.75564i 2.95786 + 9.10335i −2.88014 + 8.86415i 19.3895 + 14.0873i 18.3436
26.2 −1.81555 − 1.31908i 1.43526 − 4.41727i −0.915867 − 2.81875i −4.04508 + 2.93893i −8.43250 + 6.12657i −4.84499 − 14.9113i −7.60317 + 23.4002i 4.39116 + 3.19036i 11.2207
26.3 −0.542122 − 0.393874i −3.01008 + 9.26408i −2.33338 − 7.18140i −4.04508 + 2.93893i 5.28071 − 3.83666i −6.58487 − 20.2662i −3.22017 + 9.91067i −54.9190 − 39.9010i 3.35050
26.4 1.81396 + 1.31792i 2.45444 − 7.55399i −0.918588 − 2.82712i −4.04508 + 2.93893i 14.4078 − 10.4679i −0.510862 − 1.57227i 7.60263 − 23.3985i −29.1951 − 21.2115i −11.2109
26.5 2.85482 + 2.07415i −1.54064 + 4.74160i 1.37577 + 4.23419i −4.04508 + 2.93893i −14.2330 + 10.3409i 6.81120 + 20.9627i 3.86880 − 11.9069i 1.73428 + 1.26003i −17.6438
26.6 4.39302 + 3.19171i 1.08117 − 3.32751i 6.63942 + 20.4340i −4.04508 + 2.93893i 15.3701 − 11.1670i −8.32426 − 25.6195i −22.6286 + 69.6437i 11.9401 + 8.67497i −27.1503
31.1 −1.43124 + 4.40490i 6.70801 − 4.87365i −10.8826 − 7.90666i 1.54508 + 4.75528i 11.8672 + 36.5235i 24.3122 + 17.6639i 20.4274 − 14.8414i 12.9014 − 39.7065i −23.1579
31.2 −1.41210 + 4.34600i −5.83785 + 4.24145i −10.4216 − 7.57173i 1.54508 + 4.75528i −10.1897 − 31.3607i 6.50661 + 4.72733i 18.0477 − 13.1124i 7.74716 − 23.8433i −22.8483
31.3 −0.513572 + 1.58061i −1.60233 + 1.16416i 4.23755 + 3.07876i 1.54508 + 4.75528i −1.01717 − 3.13054i −7.13418 − 5.18329i −17.7990 + 12.9317i −7.13127 + 21.9478i −8.30978
31.4 0.267133 − 0.822150i 4.45886 − 3.23955i 5.86756 + 4.26304i 1.54508 + 4.75528i −1.47229 − 4.53124i −2.26519 − 1.64576i 10.6672 − 7.75016i 1.04327 − 3.21086i 4.32230
31.5 0.849844 − 2.61555i −5.86409 + 4.26051i 0.353259 + 0.256657i 1.54508 + 4.75528i 6.16003 + 18.9586i 24.9835 + 18.1516i 18.7709 − 13.6378i 7.89215 − 24.2895i 13.7508
31.6 1.50387 − 4.62843i 4.25544 − 3.09176i −12.6886 − 9.21884i 1.54508 + 4.75528i −7.91037 − 24.3456i 4.59294 + 3.33697i −30.2534 + 21.9804i 0.206327 − 0.635008i 24.3331
36.1 −2.96806 + 2.15642i −0.538187 − 1.65637i 1.68708 − 5.19231i −4.04508 − 2.93893i 5.16920 + 3.75564i 2.95786 − 9.10335i −2.88014 − 8.86415i 19.3895 − 14.0873i 18.3436
36.2 −1.81555 + 1.31908i 1.43526 + 4.41727i −0.915867 + 2.81875i −4.04508 − 2.93893i −8.43250 − 6.12657i −4.84499 + 14.9113i −7.60317 − 23.4002i 4.39116 − 3.19036i 11.2207
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 16.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 55.4.g.b ✓ 24
11.c even 5 1 inner 55.4.g.b ✓ 24
11.c even 5 1 605.4.a.p 12
11.d odd 10 1 605.4.a.t 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.4.g.b ✓ 24 1.a even 1 1 trivial
55.4.g.b ✓ 24 11.c even 5 1 inner
605.4.a.p 12 11.c even 5 1
605.4.a.t 12 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} - 6 T_{2}^{23} + 60 T_{2}^{22} - 290 T_{2}^{21} + 1977 T_{2}^{20} - 6286 T_{2}^{19} + \cdots + 9305303296 \) acting on \(S_{4}^{\mathrm{new}}(55, [\chi])\). Copy content Toggle raw display