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Properties

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

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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 = [26,1] 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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + q^{2} + 39 q^{3} - 55 q^{4} + 39 q^{5} + 6 q^{6} - 13 q^{7} - 108 q^{8} - 117 q^{9} + 5 q^{10} + 49 q^{11} + 165 q^{12} + 338 q^{13} + 49 q^{14} + 234 q^{15} - 223 q^{16} + 82 q^{17} + 9 q^{18}+ \cdots - 882 q^{99}+O(q^{100}) \) 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 −2.58550 + 4.47822i 1.50000 + 2.59808i −9.36964 − 16.2287i 9.12230 − 15.8003i −15.5130 −18.5179 + 0.296931i 55.5328 −4.50000 + 7.79423i 47.1714 + 81.7033i
79.2 −2.27880 + 3.94700i 1.50000 + 2.59808i −6.38586 − 11.0606i −0.0669561 + 0.115971i −13.6728 7.45965 − 16.9515i 21.7476 −4.50000 + 7.79423i −0.305159 − 0.528551i
79.3 −1.61281 + 2.79348i 1.50000 + 2.59808i −1.20234 − 2.08251i 10.7354 − 18.5943i −9.67689 17.2657 + 6.70044i −18.0484 −4.50000 + 7.79423i 34.6285 + 59.9783i
79.4 −1.52306 + 2.63802i 1.50000 + 2.59808i −0.639438 − 1.10754i −5.80782 + 10.0594i −9.13837 −6.71490 + 17.2601i −20.4734 −4.50000 + 7.79423i −17.6914 − 30.6423i
79.5 −1.21830 + 2.11016i 1.50000 + 2.59808i 1.03147 + 1.78657i −2.89639 + 5.01669i −7.30982 −14.9059 + 10.9916i −24.5194 −4.50000 + 7.79423i −7.05736 − 12.2237i
79.6 −0.659305 + 1.14195i 1.50000 + 2.59808i 3.13063 + 5.42242i 2.71825 − 4.70815i −3.95583 −0.00228984 − 18.5203i −18.8050 −4.50000 + 7.79423i 3.58431 + 6.20821i
79.7 0.312538 − 0.541331i 1.50000 + 2.59808i 3.80464 + 6.58983i 3.36814 − 5.83379i 1.87523 18.3523 − 2.48869i 9.75697 −4.50000 + 7.79423i −2.10534 − 3.64656i
79.8 0.313742 − 0.543417i 1.50000 + 2.59808i 3.80313 + 6.58722i −9.16381 + 15.8722i 1.88245 −15.3530 − 10.3579i 9.79268 −4.50000 + 7.79423i 5.75014 + 9.95954i
79.9 1.06441 − 1.84361i 1.50000 + 2.59808i 1.73406 + 3.00348i −4.68099 + 8.10772i 6.38646 18.0318 − 4.22554i 24.4136 −4.50000 + 7.79423i 9.96500 + 17.2599i
79.10 1.54835 − 2.68181i 1.50000 + 2.59808i −0.794753 − 1.37655i 6.81244 − 11.7995i 9.29008 4.33899 + 18.0048i 19.8513 −4.50000 + 7.79423i −21.0960 − 36.5394i
79.11 1.99520 − 3.45578i 1.50000 + 2.59808i −3.96161 − 6.86171i 2.82470 − 4.89253i 11.9712 −18.0591 − 4.10703i 0.306392 −4.50000 + 7.79423i −11.2717 − 19.5231i
79.12 2.35147 − 4.07287i 1.50000 + 2.59808i −7.05883 − 12.2262i −2.92941 + 5.07389i 14.1088 10.1002 + 15.5237i −28.7709 −4.50000 + 7.79423i 13.7769 + 23.8622i
79.13 2.79208 − 4.83603i 1.50000 + 2.59808i −11.5915 − 20.0770i 9.46413 − 16.3924i 16.7525 −8.49558 − 16.4568i −84.7842 −4.50000 + 7.79423i −52.8493 − 91.5377i
235.1 −2.58550 − 4.47822i 1.50000 − 2.59808i −9.36964 + 16.2287i 9.12230 + 15.8003i −15.5130 −18.5179 − 0.296931i 55.5328 −4.50000 − 7.79423i 47.1714 − 81.7033i
235.2 −2.27880 − 3.94700i 1.50000 − 2.59808i −6.38586 + 11.0606i −0.0669561 − 0.115971i −13.6728 7.45965 + 16.9515i 21.7476 −4.50000 − 7.79423i −0.305159 + 0.528551i
235.3 −1.61281 − 2.79348i 1.50000 − 2.59808i −1.20234 + 2.08251i 10.7354 + 18.5943i −9.67689 17.2657 − 6.70044i −18.0484 −4.50000 − 7.79423i 34.6285 − 59.9783i
235.4 −1.52306 − 2.63802i 1.50000 − 2.59808i −0.639438 + 1.10754i −5.80782 − 10.0594i −9.13837 −6.71490 − 17.2601i −20.4734 −4.50000 − 7.79423i −17.6914 + 30.6423i
235.5 −1.21830 − 2.11016i 1.50000 − 2.59808i 1.03147 − 1.78657i −2.89639 − 5.01669i −7.30982 −14.9059 − 10.9916i −24.5194 −4.50000 − 7.79423i −7.05736 + 12.2237i
235.6 −0.659305 − 1.14195i 1.50000 − 2.59808i 3.13063 − 5.42242i 2.71825 + 4.70815i −3.95583 −0.00228984 + 18.5203i −18.8050 −4.50000 − 7.79423i 3.58431 − 6.20821i
235.7 0.312538 + 0.541331i 1.50000 − 2.59808i 3.80464 − 6.58983i 3.36814 + 5.83379i 1.87523 18.3523 + 2.48869i 9.75697 −4.50000 − 7.79423i −2.10534 + 3.64656i
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 79.13
Significant digits:
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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.f ✓ 26
7.c even 3 1 inner 273.4.i.f ✓ 26
7.c even 3 1 1911.4.a.z 13
7.d odd 6 1 1911.4.a.ba 13
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
273.4.i.f ✓ 26 1.a even 1 1 trivial
273.4.i.f ✓ 26 7.c even 3 1 inner
1911.4.a.z 13 7.c even 3 1
1911.4.a.ba 13 7.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} - T_{2}^{25} + 80 T_{2}^{24} - 33 T_{2}^{23} + 3955 T_{2}^{22} - 783 T_{2}^{21} + \cdots + 40642560000 \) acting on \(S_{4}^{\mathrm{new}}(273, [\chi])\). Copy content Toggle raw display