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Properties

Label 187.3.q.a
Level $187$
Weight $3$
Character orbit 187.q
Analytic conductor $5.095$
Analytic rank $0$
Dimension $544$
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] = [187,3,Mod(2,187)] 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("187.2"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([4, 35])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 187.q (of order \(40\), degree \(16\), 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: \(5.09538094354\)
Analytic rank: \(0\)
Dimension: \(544\)
Relative dimension: \(34\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 544 q - 20 q^{2} - 12 q^{3} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 36 q^{9} + 28 q^{11} - 200 q^{12} + 36 q^{14} + 108 q^{15} + 424 q^{16} - 180 q^{17} - 40 q^{18} - 20 q^{19} - 140 q^{20} + 32 q^{22}+ \cdots - 72 q^{99}+O(q^{100}) \) 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 −1.78353 − 3.50038i 0.321032 − 0.523876i −6.72053 + 9.25001i 4.15293 − 3.54694i −2.40634 − 0.189383i 3.93050 + 6.41399i 28.8440 + 4.56844i 3.91453 + 7.68270i −19.8225 − 8.21076i
2.2 −1.69946 − 3.33538i 2.52468 − 4.11991i −5.88545 + 8.10063i −4.99610 + 4.26708i −18.0321 − 1.41915i −2.07016 − 3.37819i 22.2316 + 3.52114i −6.51371 − 12.7839i 22.7230 + 9.41218i
2.3 −1.55829 − 3.05832i −0.816956 + 1.33315i −4.57391 + 6.29545i −2.50010 + 2.13529i 5.35026 + 0.421074i −0.500284 − 0.816389i 12.8203 + 2.03054i 2.97604 + 5.84081i 10.4263 + 4.31871i
2.4 −1.45677 − 2.85908i −2.87882 + 4.69781i −3.70100 + 5.09399i 2.00014 − 1.70828i 17.6252 + 1.38713i 4.54048 + 7.40939i 7.27838 + 1.15278i −9.69589 − 19.0293i −7.79786 − 3.22998i
2.5 −1.44027 − 2.82668i −1.80943 + 2.95272i −3.56462 + 4.90629i 2.69247 − 2.29959i 10.9525 + 0.861978i −6.62694 − 10.8142i 6.46891 + 1.02458i −1.35861 − 2.66642i −10.3781 − 4.29874i
2.6 −1.35588 − 2.66107i 1.29183 − 2.10808i −2.89174 + 3.98014i 3.25875 − 2.78323i −7.36132 − 0.579349i −2.32622 − 3.79605i 2.71304 + 0.429703i 1.31075 + 2.57249i −11.8249 − 4.89802i
2.7 −1.18013 − 2.31613i 3.02186 − 4.93123i −1.62062 + 2.23059i 4.10263 − 3.50397i −14.9876 − 1.17955i 5.31030 + 8.66563i −3.19092 − 0.505391i −11.0995 − 21.7839i −12.9573 − 5.36709i
2.8 −1.16003 − 2.27670i 0.682188 − 1.11323i −1.48652 + 2.04603i −3.34754 + 2.85907i −3.32585 − 0.261750i 6.33486 + 10.3376i −3.71235 − 0.587978i 3.31202 + 6.50020i 10.3925 + 4.30471i
2.9 −1.14630 − 2.24974i 0.403742 − 0.658847i −1.39618 + 1.92167i −5.33542 + 4.55688i −1.94504 − 0.153078i −2.64570 − 4.31739i −4.05172 − 0.641729i 3.81484 + 7.48705i 16.3678 + 6.77975i
2.10 −0.847931 − 1.66416i −1.35386 + 2.20930i 0.300703 − 0.413883i −0.447824 + 0.382478i 4.82460 + 0.379704i 2.34605 + 3.82841i −8.32268 − 1.31818i 1.03786 + 2.03691i 1.01623 + 0.420935i
2.11 −0.799753 − 1.56960i −1.42531 + 2.32590i 0.527090 − 0.725477i 6.74980 − 5.76487i 4.79063 + 0.377031i 2.14971 + 3.50801i −8.51993 − 1.34942i 0.707634 + 1.38881i −14.4467 − 5.98403i
2.12 −0.790084 − 1.55063i −2.75520 + 4.49607i 0.570931 − 0.785819i −6.50583 + 5.55651i 9.14857 + 0.720008i −0.337596 − 0.550907i −8.54513 − 1.35341i −8.53766 − 16.7561i 13.7562 + 5.69801i
2.13 −0.742878 − 1.45798i 2.02567 − 3.30559i 0.777301 − 1.06986i 0.217735 − 0.185963i −6.32431 − 0.497734i −3.29328 − 5.37415i −8.60202 − 1.36243i −2.73767 − 5.37298i −0.432881 − 0.179305i
2.14 −0.526382 − 1.03308i 0.640671 − 1.04548i 1.56096 − 2.14848i 4.83800 − 4.13204i −1.41731 − 0.111544i −3.11140 − 5.07734i −7.62194 − 1.20720i 3.40334 + 6.67944i −6.81537 − 2.82302i
2.15 −0.294962 − 0.578895i 2.40623 − 3.92662i 2.10302 − 2.89456i −6.23328 + 5.32372i −2.98285 − 0.234755i −1.05606 − 1.72334i −4.86280 − 0.770193i −5.54244 − 10.8776i 4.92046 + 2.03812i
2.16 −0.273063 − 0.535917i −1.28016 + 2.08903i 2.13850 − 2.94339i −2.56895 + 2.19409i 1.46911 + 0.115621i −4.49822 − 7.34043i −4.53763 − 0.718690i 1.36069 + 2.67050i 1.87733 + 0.777617i
2.17 −0.0206482 − 0.0405244i 0.427119 − 0.696996i 2.34993 − 3.23439i −1.14178 + 0.975172i −0.0370646 − 0.00291705i 6.06168 + 9.89176i −0.359280 − 0.0569044i 3.78254 + 7.42366i 0.0630940 + 0.0261344i
2.18 0.0738746 + 0.144987i −1.98602 + 3.24089i 2.33558 − 3.21465i −0.527290 + 0.450348i −0.616605 − 0.0485279i 2.22828 + 3.63622i 1.28150 + 0.202970i −2.47320 − 4.85392i −0.104248 − 0.0431810i
2.19 0.0959067 + 0.188228i 1.40645 − 2.29512i 2.32491 − 3.19996i 4.80267 − 4.10187i 0.566893 + 0.0446154i 2.40321 + 3.92168i 1.65990 + 0.262903i 0.796444 + 1.56311i 1.23269 + 0.510599i
2.20 0.188210 + 0.369383i −2.91302 + 4.75361i 2.25012 − 3.09702i 5.79055 − 4.94560i −2.30417 − 0.181342i −3.48376 − 5.68498i 3.20534 + 0.507677i −10.0252 − 19.6756i 2.91667 + 1.20812i
See next 80 embeddings (of 544 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
11.d odd 10 1 inner
17.d even 8 1 inner
187.q odd 40 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 187.3.q.a ✓ 544
11.d odd 10 1 inner 187.3.q.a ✓ 544
17.d even 8 1 inner 187.3.q.a ✓ 544
187.q odd 40 1 inner 187.3.q.a ✓ 544
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
187.3.q.a ✓ 544 1.a even 1 1 trivial
187.3.q.a ✓ 544 11.d odd 10 1 inner
187.3.q.a ✓ 544 17.d even 8 1 inner
187.3.q.a ✓ 544 187.q odd 40 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(187, [\chi])\).