Properties

Label 182.3.k.a
Level 182182
Weight 33
Character orbit 182.k
Analytic conductor 4.9594.959
Analytic rank 00
Dimension 3636
Inner twists 22

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [182,3,Mod(101,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) 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("182.101"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 182=2713 182 = 2 \cdot 7 \cdot 13
Weight: k k == 3 3
Character orbit: [χ][\chi] == 182.k (of order 66, degree 22, 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: 4.959140811364.95914081136
Analytic rank: 00
Dimension: 3636
Relative dimension: 1818 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

qq-expansion

The algebraic qq-expansion of this newform has not been computed, but we have computed the trace expansion.

Tr(f)(q)=\operatorname{Tr}(f)(q) = 36q+36q4+10q788q912q124q1312q14+60q1572q16+24q1724q18+100q1942q21+12q22+28q2382q25+120q26+4q28++96q98+O(q100) 36 q + 36 q^{4} + 10 q^{7} - 88 q^{9} - 12 q^{12} - 4 q^{13} - 12 q^{14} + 60 q^{15} - 72 q^{16} + 24 q^{17} - 24 q^{18} + 100 q^{19} - 42 q^{21} + 12 q^{22} + 28 q^{23} - 82 q^{25} + 120 q^{26} + 4 q^{28}+ \cdots + 96 q^{98}+O(q^{100}) Copy content Toggle raw display

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\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   a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
101.1 −1.22474 0.707107i 5.39170i 1.00000 + 1.73205i 1.60444 + 2.77896i −3.81251 + 6.60346i −6.78200 1.73332i 2.82843i −20.0704 4.53803i
101.2 −1.22474 0.707107i 3.15670i 1.00000 + 1.73205i 2.18358 + 3.78206i −2.23213 + 3.86616i 5.93564 + 3.71055i 2.82843i −0.964772 6.17609i
101.3 −1.22474 0.707107i 2.74178i 1.00000 + 1.73205i −0.905631 1.56860i −1.93873 + 3.35798i 6.97908 0.540725i 2.82843i 1.48266 2.56151i
101.4 −1.22474 0.707107i 0.464638i 1.00000 + 1.73205i 0.913880 + 1.58289i −0.328548 + 0.569062i −5.23853 4.64303i 2.82843i 8.78411 2.58484i
101.5 −1.22474 0.707107i 0.599163i 1.00000 + 1.73205i −2.93203 5.07842i 0.423672 0.733822i −6.63379 + 2.23447i 2.82843i 8.64100 8.29303i
101.6 −1.22474 0.707107i 0.997088i 1.00000 + 1.73205i −2.39328 4.14528i 0.705048 1.22118i 0.359568 + 6.99076i 2.82843i 8.00582 6.76921i
101.7 −1.22474 0.707107i 2.61846i 1.00000 + 1.73205i 3.10639 + 5.38043i 1.85153 3.20695i 2.61741 6.49224i 2.82843i 2.14365 8.78621i
101.8 −1.22474 0.707107i 4.37470i 1.00000 + 1.73205i 2.56440 + 4.44167i 3.09338 5.35789i 2.86286 + 6.38780i 2.82843i −10.1380 7.25322i
101.9 −1.22474 0.707107i 4.89745i 1.00000 + 1.73205i −4.14175 7.17372i 3.46302 5.99813i 4.84926 5.04824i 2.82843i −14.9850 11.7146i
101.10 1.22474 + 0.707107i 4.24411i 1.00000 + 1.73205i −2.97543 5.15360i 3.00104 5.19795i −6.87300 1.32736i 2.82843i −9.01248 8.41579i
101.11 1.22474 + 0.707107i 3.98808i 1.00000 + 1.73205i 0.700844 + 1.21390i 2.82000 4.88438i 2.68579 6.46425i 2.82843i −6.90481 1.98229i
101.12 1.22474 + 0.707107i 3.43880i 1.00000 + 1.73205i 3.24452 + 5.61967i 2.43160 4.21165i 3.70893 + 5.93665i 2.82843i −2.82532 9.17688i
101.13 1.22474 + 0.707107i 0.262462i 1.00000 + 1.73205i −4.53203 7.84970i 0.185589 0.321449i 6.48718 + 2.62991i 2.82843i 8.93111 12.8185i
101.14 1.22474 + 0.707107i 0.0568985i 1.00000 + 1.73205i 0.904458 + 1.56657i 0.0402333 0.0696861i 2.86528 6.38672i 2.82843i 8.99676 2.55819i
101.15 1.22474 + 0.707107i 0.265126i 1.00000 + 1.73205i 1.03292 + 1.78906i −0.187472 + 0.324711i −5.02643 + 4.87186i 2.82843i 8.92971 2.92153i
101.16 1.22474 + 0.707107i 3.89692i 1.00000 + 1.73205i 0.569657 + 0.986676i −2.75554 + 4.77274i 6.85176 + 1.43295i 2.82843i −6.18601 1.61123i
101.17 1.22474 + 0.707107i 4.02925i 1.00000 + 1.73205i 4.59702 + 7.96227i −2.84911 + 4.93480i −5.39829 4.45628i 2.82843i −7.23484 13.0023i
101.18 1.22474 + 0.707107i 5.53110i 1.00000 + 1.73205i −3.54195 6.13483i −3.91108 + 6.77419i −5.25071 + 4.62926i 2.82843i −21.5931 10.0181i
173.1 −1.22474 + 0.707107i 4.89745i 1.00000 1.73205i −4.14175 + 7.17372i 3.46302 + 5.99813i 4.84926 + 5.04824i 2.82843i −14.9850 11.7146i
173.2 −1.22474 + 0.707107i 4.37470i 1.00000 1.73205i 2.56440 4.44167i 3.09338 + 5.35789i 2.86286 6.38780i 2.82843i −10.1380 7.25322i
See all 36 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 101.18
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
91.p odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 182.3.k.a 36
7.d odd 6 1 182.3.r.a yes 36
13.e even 6 1 182.3.r.a yes 36
91.p odd 6 1 inner 182.3.k.a 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
182.3.k.a 36 1.a even 1 1 trivial
182.3.k.a 36 91.p odd 6 1 inner
182.3.r.a yes 36 7.d odd 6 1
182.3.r.a yes 36 13.e even 6 1

Hecke kernels

This newform subspace is the entire newspace S3new(182,[χ])S_{3}^{\mathrm{new}}(182, [\chi]).