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Properties

Label 92.5.f.a
Level $92$
Weight $5$
Character orbit 92.f
Analytic conductor $9.510$
Analytic rank $0$
Dimension $80$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [92,5,Mod(5,92)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.5");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 92.f (of order \(22\), 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: \(9.51003660371\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q + 10 q^{3} - 318 q^{9} + 2 q^{13} + 1463 q^{15} - 495 q^{17} - 957 q^{19} - 1353 q^{21} + 1614 q^{23} + 1890 q^{25} + 4723 q^{27} - 1617 q^{29} - 3271 q^{31} - 6655 q^{33} - 5280 q^{35} + 3520 q^{37}+ \cdots - 48477 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 0 −10.2373 + 11.8144i 0 −30.5407 − 4.39110i 0 −13.3522 + 6.09777i 0 −23.2517 − 161.719i 0
5.2 0 −6.76620 + 7.80861i 0 32.0322 + 4.60554i 0 17.3862 − 7.93999i 0 −3.66545 − 25.4937i 0
5.3 0 −4.95559 + 5.71906i 0 −3.34342 − 0.480711i 0 −14.6603 + 6.69511i 0 3.37777 + 23.4929i 0
5.4 0 0.325960 − 0.376178i 0 −35.7139 − 5.13488i 0 57.8313 − 26.4107i 0 11.4922 + 79.9303i 0
5.5 0 3.01425 − 3.47863i 0 7.38497 + 1.06180i 0 35.2368 − 16.0921i 0 8.51233 + 59.2046i 0
5.6 0 3.34179 − 3.85663i 0 −4.69485 − 0.675018i 0 −82.0191 + 37.4569i 0 7.82145 + 54.3994i 0
5.7 0 7.42513 − 8.56905i 0 47.6796 + 6.85529i 0 11.7029 − 5.34454i 0 −6.76867 − 47.0771i 0
5.8 0 10.5723 − 12.2011i 0 −24.5957 − 3.53633i 0 14.8856 − 6.79802i 0 −25.5654 − 177.811i 0
17.1 0 −13.2407 − 3.88781i 0 4.37705 + 6.81083i 0 −71.4769 − 10.2768i 0 92.0587 + 59.1625i 0
17.2 0 −9.91432 − 2.91111i 0 −22.1926 − 34.5324i 0 38.0772 + 5.47467i 0 21.6776 + 13.9314i 0
17.3 0 −9.85031 − 2.89231i 0 8.29543 + 12.9079i 0 46.9607 + 6.75193i 0 20.5215 + 13.1884i 0
17.4 0 0.536308 + 0.157474i 0 3.14686 + 4.89660i 0 −55.6751 − 8.00488i 0 −67.8787 − 43.6230i 0
17.5 0 2.34060 + 0.687262i 0 21.9968 + 34.2277i 0 22.5786 + 3.24631i 0 −63.1355 − 40.5747i 0
17.6 0 4.86802 + 1.42938i 0 −8.73770 − 13.5961i 0 51.3576 + 7.38410i 0 −46.4871 − 29.8754i 0
17.7 0 8.15848 + 2.39555i 0 −18.7036 − 29.1033i 0 −54.6689 − 7.86020i 0 −7.31931 − 4.70383i 0
17.8 0 15.7364 + 4.62062i 0 6.12535 + 9.53123i 0 6.79278 + 0.976655i 0 158.142 + 101.632i 0
21.1 0 −2.44568 − 17.0101i 0 −12.8263 + 43.6825i 0 44.6142 + 38.6584i 0 −205.644 + 60.3824i 0
21.2 0 −1.70114 − 11.8317i 0 6.41533 − 21.8486i 0 −35.1057 − 30.4192i 0 −59.3762 + 17.4344i 0
21.3 0 −0.996463 − 6.93055i 0 5.74873 − 19.5784i 0 56.9158 + 49.3178i 0 30.6793 − 9.00825i 0
21.4 0 −0.369021 − 2.56660i 0 −3.51259 + 11.9628i 0 −6.50335 − 5.63519i 0 71.2677 − 20.9261i 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.d odd 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 92.5.f.a ✓ 80
23.d odd 22 1 inner 92.5.f.a ✓ 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
92.5.f.a ✓ 80 1.a even 1 1 trivial
92.5.f.a ✓ 80 23.d odd 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(92, [\chi])\).