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Properties

Label 153.3.q.a
Level $153$
Weight $3$
Character orbit 153.q
Analytic conductor $4.169$
Analytic rank $0$
Dimension $272$
Inner twists $4$

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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] = [153,3,Mod(2,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 21])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.2"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 153.q (of order \(24\), degree \(8\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.16894804471\)
Analytic rank: \(0\)
Dimension: \(272\)
Relative dimension: \(34\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −0.976788 − 3.64542i 2.89472 + 0.787774i −8.87089 + 5.12161i 6.48194 + 4.97377i 0.0442393 − 11.3220i 0.354599 + 0.462123i 16.6609 + 16.6609i 7.75882 + 4.56077i 11.8000 − 28.4877i
2.2 −0.958970 − 3.57893i −2.63450 + 1.43507i −8.42499 + 4.86417i −3.62363 − 2.78051i 7.66241 + 8.05249i 6.54948 + 8.53545i 15.0080 + 15.0080i 4.88116 − 7.56137i −6.47627 + 15.6351i
2.3 −0.952810 − 3.55594i −1.96843 − 2.26391i −8.27274 + 4.77627i 0.135821 + 0.104219i −6.17477 + 9.15669i −6.27549 − 8.17838i 14.4539 + 14.4539i −1.25055 + 8.91270i 0.241185 − 0.582272i
2.4 −0.879999 − 3.28420i 2.86641 − 0.885249i −6.54748 + 3.78019i −7.23778 − 5.55374i −5.42978 − 8.63487i 0.237850 + 0.309972i 8.55988 + 8.55988i 7.43267 − 5.07498i −11.8704 + 28.6576i
2.5 −0.826656 − 3.08512i 0.255503 + 2.98910i −5.37052 + 3.10067i −0.912220 − 0.699971i 9.01052 − 3.25922i −4.84982 − 6.32041i 4.97164 + 4.97164i −8.86944 + 1.52745i −1.40540 + 3.39294i
2.6 −0.711546 − 2.65552i 1.11729 − 2.78418i −3.08141 + 1.77905i 1.90049 + 1.45830i −8.18846 − 0.985928i −0.864006 − 1.12599i −0.859030 − 0.859030i −6.50331 − 6.22149i 2.52026 − 6.08445i
2.7 −0.687998 − 2.56764i −2.75883 − 1.17849i −2.65535 + 1.53307i 6.46936 + 4.96411i −1.12787 + 7.89450i 6.24766 + 8.14211i −1.75533 − 1.75533i 6.22233 + 6.50251i 8.29517 − 20.0263i
2.8 −0.664763 − 2.48093i 1.32721 + 2.69045i −2.24900 + 1.29846i 0.0683317 + 0.0524328i 5.79253 − 5.08123i 6.43430 + 8.38534i −2.54823 − 2.54823i −5.47702 + 7.14158i 0.0846576 − 0.204381i
2.9 −0.647250 − 2.41557i −2.31487 + 1.90824i −1.95194 + 1.12695i 3.78501 + 2.90434i 6.10779 + 4.35662i −3.37531 − 4.39879i −3.08765 − 3.08765i 1.71724 − 8.83465i 4.56579 − 11.0228i
2.10 −0.559970 − 2.08984i −1.00314 − 2.82732i −0.589750 + 0.340492i −5.27616 − 4.04854i −5.34690 + 3.67960i 3.14801 + 4.10257i −5.07765 − 5.07765i −6.98743 + 5.67237i −5.50630 + 13.2934i
2.11 −0.455624 − 1.70041i 2.67577 − 1.35656i 0.780296 − 0.450504i 2.73244 + 2.09667i −3.52586 − 3.93183i −1.58154 − 2.06110i −6.10071 − 6.10071i 5.31948 − 7.25969i 2.32024 − 5.60156i
2.12 −0.343290 − 1.28118i −2.90483 − 0.749645i 1.94054 − 1.12037i −2.44044 − 1.87262i 0.0367716 + 3.97895i −0.900245 − 1.17322i −5.85310 − 5.85310i 7.87606 + 4.35518i −1.56137 + 3.76949i
2.13 −0.322956 − 1.20529i 2.45139 + 1.72936i 2.11568 − 1.22149i −4.43241 − 3.40111i 1.29268 − 3.51314i −7.76060 − 10.1138i −5.68485 − 5.68485i 3.01864 + 8.47867i −2.66784 + 6.44074i
2.14 −0.244444 − 0.912279i −1.06612 + 2.80417i 2.69160 − 1.55400i −6.37893 − 4.89473i 2.81880 + 0.287134i 2.10063 + 2.73760i −4.74697 − 4.74697i −6.72678 − 5.97917i −2.90606 + 7.01586i
2.15 −0.204085 − 0.761655i 2.97697 + 0.370973i 2.92563 − 1.68912i −0.546192 − 0.419108i −0.325002 − 2.34314i 6.84367 + 8.91884i −4.11388 − 4.11388i 8.72476 + 2.20875i −0.207746 + 0.501543i
2.16 −0.141239 − 0.527112i 1.73795 + 2.44531i 3.20620 − 1.85110i 7.66759 + 5.88355i 1.04348 − 1.26147i −3.59594 − 4.68632i −2.97207 − 2.97207i −2.95905 + 8.49965i 2.01832 − 4.87267i
2.17 −0.0836437 − 0.312162i −1.97783 + 2.25570i 3.37365 − 1.94778i 2.39152 + 1.83508i 0.869578 + 0.428729i 0.429766 + 0.560082i −1.80428 − 1.80428i −1.17638 − 8.92279i 0.372807 − 0.900036i
2.18 −0.00739618 − 0.0276029i −0.351156 − 2.97938i 3.46339 − 1.99959i −1.61331 − 1.23794i −0.0796423 + 0.0317290i −6.12912 − 7.98762i −0.161637 − 0.161637i −8.75338 + 2.09245i −0.0222383 + 0.0536881i
2.19 0.0361624 + 0.134960i −0.00871697 − 2.99999i 3.44720 − 1.99024i 4.35972 + 3.34533i 0.404563 − 0.109663i 6.08938 + 7.93584i 0.788451 + 0.788451i −8.99985 + 0.0523016i −0.293828 + 0.709363i
2.20 0.0775060 + 0.289257i −2.82295 − 1.01536i 3.38644 − 1.95516i 2.93290 + 2.25049i 0.0749028 − 0.895253i −2.95513 − 3.85120i 1.67501 + 1.67501i 6.93810 + 5.73260i −0.423652 + 1.02279i
See next 80 embeddings (of 272 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.34
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.d odd 6 1 inner
17.d even 8 1 inner
153.q odd 24 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 153.3.q.a ✓ 272
9.d odd 6 1 inner 153.3.q.a ✓ 272
17.d even 8 1 inner 153.3.q.a ✓ 272
153.q odd 24 1 inner 153.3.q.a ✓ 272
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
153.3.q.a ✓ 272 1.a even 1 1 trivial
153.3.q.a ✓ 272 9.d odd 6 1 inner
153.3.q.a ✓ 272 17.d even 8 1 inner
153.3.q.a ✓ 272 153.q odd 24 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(153, [\chi])\).