↑

Properties

Label 273.4.i.e
Level $273$
Weight $4$
Character orbit 273.i
Analytic conductor $16.108$
Analytic rank $0$
Dimension $26$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [273,4,Mod(79,273)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("273.79"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [26,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(16.1075214316\)
Analytic rank: \(0\)
Dimension: \(26\)
Relative dimension: \(13\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 3 q^{2} - 39 q^{3} - 55 q^{4} - 15 q^{5} + 18 q^{6} - 13 q^{7} - 12 q^{8} - 117 q^{9} - 11 q^{10} - 57 q^{11} - 165 q^{12} + 338 q^{13} + 105 q^{14} + 90 q^{15} - 311 q^{16} - 162 q^{17} - 27 q^{18}+ \cdots + 1026 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
79.1 −2.60349 + 4.50939i −1.50000 − 2.59808i −9.55637 − 16.5521i −6.56971 + 11.3791i 15.6210 17.5623 − 5.87916i 57.8639 −4.50000 + 7.79423i −34.2084 − 59.2507i
79.2 −2.42742 + 4.20442i −1.50000 − 2.59808i −7.78477 − 13.4836i −2.12186 + 3.67518i 14.5645 −14.6768 + 11.2957i 36.7489 −4.50000 + 7.79423i −10.3013 − 17.8424i
79.3 −2.18545 + 3.78531i −1.50000 − 2.59808i −5.55236 − 9.61696i 8.51830 − 14.7541i 13.1127 6.69768 − 17.2668i 13.5704 −4.50000 + 7.79423i 37.2326 + 64.4887i
79.4 −1.28882 + 2.23230i −1.50000 − 2.59808i 0.677903 + 1.17416i −8.22657 + 14.2488i 7.73290 −10.1226 − 15.5091i −24.1158 −4.50000 + 7.79423i −21.2051 − 36.7283i
79.5 −1.16895 + 2.02468i −1.50000 − 2.59808i 1.26712 + 2.19472i 2.04753 − 3.54642i 7.01369 9.66697 + 15.7971i −24.6280 −4.50000 + 7.79423i 4.78691 + 8.29117i
79.6 −0.830986 + 1.43931i −1.50000 − 2.59808i 2.61893 + 4.53611i 7.38335 − 12.7883i 4.98591 −18.4901 + 1.05688i −22.0009 −4.50000 + 7.79423i 12.2709 + 21.2539i
79.7 −0.0371423 + 0.0643323i −1.50000 − 2.59808i 3.99724 + 6.92342i 7.03450 − 12.1841i 0.222854 11.4953 − 14.5209i −1.18814 −4.50000 + 7.79423i 0.522555 + 0.905091i
79.8 −0.0163346 + 0.0282923i −1.50000 − 2.59808i 3.99947 + 6.92728i −10.9115 + 18.8993i 0.0980076 13.3977 + 12.7868i −0.522672 −4.50000 + 7.79423i −0.356470 − 0.617423i
79.9 0.896185 − 1.55224i −1.50000 − 2.59808i 2.39370 + 4.14602i −0.238290 + 0.412731i −5.37711 −17.3425 + 6.49897i 22.9198 −4.50000 + 7.79423i 0.427104 + 0.739767i
79.10 1.31769 − 2.28230i −1.50000 − 2.59808i 0.527396 + 0.913477i −4.87831 + 8.44947i −7.90613 −1.28955 − 18.4753i 23.8628 −4.50000 + 7.79423i 12.8562 + 22.2675i
79.11 1.74807 − 3.02775i −1.50000 − 2.59808i −2.11152 − 3.65725i −2.96896 + 5.14238i −10.4884 18.5071 + 0.698453i 13.2048 −4.50000 + 7.79423i 10.3799 + 17.9785i
79.12 2.53300 − 4.38729i −1.50000 − 2.59808i −8.83220 − 15.2978i −5.06808 + 8.77817i −15.1980 −18.4941 + 0.983866i −48.9599 −4.50000 + 7.79423i 25.6749 + 44.4703i
79.13 2.56364 − 4.44036i −1.50000 − 2.59808i −9.14454 − 15.8388i 8.49958 − 14.7217i −15.3819 −3.41145 + 18.2034i −52.7551 −4.50000 + 7.79423i −43.5798 − 75.4824i
235.1 −2.60349 − 4.50939i −1.50000 + 2.59808i −9.55637 + 16.5521i −6.56971 − 11.3791i 15.6210 17.5623 + 5.87916i 57.8639 −4.50000 − 7.79423i −34.2084 + 59.2507i
235.2 −2.42742 − 4.20442i −1.50000 + 2.59808i −7.78477 + 13.4836i −2.12186 − 3.67518i 14.5645 −14.6768 − 11.2957i 36.7489 −4.50000 − 7.79423i −10.3013 + 17.8424i
235.3 −2.18545 − 3.78531i −1.50000 + 2.59808i −5.55236 + 9.61696i 8.51830 + 14.7541i 13.1127 6.69768 + 17.2668i 13.5704 −4.50000 − 7.79423i 37.2326 − 64.4887i
235.4 −1.28882 − 2.23230i −1.50000 + 2.59808i 0.677903 − 1.17416i −8.22657 − 14.2488i 7.73290 −10.1226 + 15.5091i −24.1158 −4.50000 − 7.79423i −21.2051 + 36.7283i
235.5 −1.16895 − 2.02468i −1.50000 + 2.59808i 1.26712 − 2.19472i 2.04753 + 3.54642i 7.01369 9.66697 − 15.7971i −24.6280 −4.50000 − 7.79423i 4.78691 − 8.29117i
235.6 −0.830986 − 1.43931i −1.50000 + 2.59808i 2.61893 − 4.53611i 7.38335 + 12.7883i 4.98591 −18.4901 − 1.05688i −22.0009 −4.50000 − 7.79423i 12.2709 − 21.2539i
235.7 −0.0371423 − 0.0643323i −1.50000 + 2.59808i 3.99724 − 6.92342i 7.03450 + 12.1841i 0.222854 11.4953 + 14.5209i −1.18814 −4.50000 − 7.79423i 0.522555 − 0.905091i
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 79.13
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 273.4.i.e ✓ 26
7.c even 3 1 inner 273.4.i.e ✓ 26
7.c even 3 1 1911.4.a.bc 13
7.d odd 6 1 1911.4.a.bb 13
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
273.4.i.e ✓ 26 1.a even 1 1 trivial
273.4.i.e ✓ 26 7.c even 3 1 inner
1911.4.a.bb 13 7.d odd 6 1
1911.4.a.bc 13 7.c even 3 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} + 3 T_{2}^{25} + 84 T_{2}^{24} + 215 T_{2}^{23} + 4261 T_{2}^{22} + 10113 T_{2}^{21} + \cdots + 1327104 \) acting on \(S_{4}^{\mathrm{new}}(273, [\chi])\). Copy content Toggle raw display