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Properties

Label 833.2.l.e
Level 833833
Weight 22
Character orbit 833.l
Analytic conductor 6.6526.652
Analytic rank 00
Dimension 4040
Inner twists 22

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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] = [833,2,Mod(246,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.246"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 833=72⋅17 833 = 7^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 833.l (of order 88, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [40,0,4,0,8,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.651538488376.65153848837
Analytic rank: 00
Dimension: 4040
Relative dimension: 1010 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

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) = 40q+4q3+8q5+12q6+20q10−12q12−8q15−64q16−16q17+24q18−8q19−20q20−8q23−12q24−8q27+8q29+36q31+72q33−8q34+⋯−16q99+O(q100) 40 q + 4 q^{3} + 8 q^{5} + 12 q^{6} + 20 q^{10} - 12 q^{12} - 8 q^{15} - 64 q^{16} - 16 q^{17} + 24 q^{18} - 8 q^{19} - 20 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{27} + 8 q^{29} + 36 q^{31} + 72 q^{33} - 8 q^{34}+ \cdots - 16 q^{99}+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}
246.1 −1.95942 + 1.95942i −0.254819 + 0.615187i − 5.67866i −3.24075 − 1.34236i −0.706112 − 1.70471i 0 7.20803 + 7.20803i 1.80780 + 1.80780i 8.98024 − 3.71974i
246.2 −1.69446 + 1.69446i 1.21869 − 2.94219i − 3.74242i 2.77390 + 1.14899i 2.92040 + 7.05047i 0 2.95248 + 2.95248i −5.04993 − 5.04993i −6.64720 + 2.75336i
246.3 −1.12834 + 1.12834i −1.18584 + 2.86288i − 0.546294i 0.640992 + 0.265507i −1.89226 − 4.56832i 0 −1.64027 − 1.64027i −4.66852 − 4.66852i −1.02284 + 0.423673i
246.4 −1.05751 + 1.05751i 0.0340087 − 0.0821043i − 0.236636i −0.164913 − 0.0683090i 0.0508614 + 0.122790i 0 −1.86477 − 1.86477i 2.11574 + 2.11574i 0.246633 − 0.102159i
246.5 −0.442594 + 0.442594i 0.937552 − 2.26345i 1.60822i −2.53962 − 1.05194i 0.586835 + 1.41674i 0 −1.59698 − 1.59698i −2.12288 − 2.12288i 1.58960 − 0.658435i
246.6 0.0415381 − 0.0415381i 0.277987 − 0.671119i 1.99655i 3.59216 + 1.48792i −0.0163300 − 0.0394241i 0 0.166009 + 0.166009i 1.74820 + 1.74820i 0.211017 − 0.0874061i
246.7 0.596796 − 0.596796i −0.794990 + 1.91928i 1.28767i −1.23190 − 0.510271i 0.670969 + 1.61986i 0 1.96207 + 1.96207i −0.930290 − 0.930290i −1.03972 + 0.430667i
246.8 0.911810 − 0.911810i 0.494163 − 1.19301i 0.337205i −1.81755 − 0.752852i −0.637220 − 1.53839i 0 2.13109 + 2.13109i 0.942233 + 0.942233i −2.34371 + 0.970799i
246.9 1.59429 − 1.59429i −0.762350 + 1.84048i − 3.08354i 2.46979 + 1.02302i 1.71885 + 4.14967i 0 −1.72748 − 1.72748i −0.684852 − 0.684852i 5.56856 − 2.30657i
246.10 1.72367 − 1.72367i 1.03560 − 2.50015i − 3.94209i 1.51788 + 0.628728i −2.52441 − 6.09448i 0 −3.34753 − 3.34753i −3.05698 − 3.05698i 3.70005 − 1.53261i
393.1 −1.81730 − 1.81730i −0.485593 + 0.201139i 4.60519i −0.362864 − 0.876031i 1.24800 + 0.516938i 0 4.73441 − 4.73441i −1.92598 + 1.92598i −0.932581 + 2.25145i
393.2 −1.32640 − 1.32640i 2.38067 − 0.986105i 1.51870i 1.04485 + 2.52249i −4.46570 − 1.84976i 0 −0.638403 + 0.638403i 2.57386 − 2.57386i 1.95995 − 4.73174i
393.3 −1.17050 − 1.17050i −3.11769 + 1.29139i 0.740157i 0.977649 + 2.36025i 5.16084 + 2.13769i 0 −1.47465 + 1.47465i 5.93098 − 5.93098i 1.61834 − 3.90703i
393.4 −0.594587 − 0.594587i −0.328149 + 0.135924i − 1.29293i 0.0662679 + 0.159985i 0.275932 + 0.114295i 0 −1.95794 + 1.95794i −2.03211 + 2.03211i 0.0557230 − 0.134527i
393.5 0.192913 + 0.192913i −1.15526 + 0.478523i − 1.92557i −0.00787468 − 0.0190112i −0.315177 − 0.130551i 0 0.757293 − 0.757293i −1.01569 + 1.01569i 0.00214837 − 0.00518662i
393.6 0.387074 + 0.387074i 2.46012 − 1.01902i − 1.70035i −1.41037 − 3.40494i 1.34668 + 0.557815i 0 1.43231 − 1.43231i 2.89249 − 2.89249i 0.772045 − 1.86388i
393.7 0.751304 + 0.751304i 1.42979 − 0.592240i − 0.871085i 1.27926 + 3.08842i 1.51916 + 0.629258i 0 2.15706 − 2.15706i −0.427757 + 0.427757i −1.35922 + 3.28146i
393.8 1.39523 + 1.39523i −0.814725 + 0.337470i 1.89333i −1.04210 − 2.51586i −1.60758 − 0.665880i 0 0.148823 − 0.148823i −1.57143 + 1.57143i 2.05623 − 4.96417i
393.9 1.64187 + 1.64187i −2.08578 + 0.863957i 3.39150i 1.37286 + 3.31438i −4.84309 − 2.00607i 0 −2.28467 + 2.28467i 1.48272 − 1.48272i −3.18773 + 7.69585i
393.10 1.95462 + 1.95462i 2.71660 − 1.12525i 5.64106i 0.0823193 + 0.198736i 7.50936 + 3.11048i 0 −7.11687 + 7.11687i 3.99241 − 3.99241i −0.227551 + 0.549356i
See all 40 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 246.10
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.d even 8 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.l.e yes 40
7.b odd 2 1 833.2.l.d ✓ 40
7.c even 3 2 833.2.v.g 80
7.d odd 6 2 833.2.v.h 80
17.d even 8 1 inner 833.2.l.e yes 40
119.l odd 8 1 833.2.l.d ✓ 40
119.q even 24 2 833.2.v.g 80
119.r odd 24 2 833.2.v.h 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.l.d ✓ 40 7.b odd 2 1
833.2.l.d ✓ 40 119.l odd 8 1
833.2.l.e yes 40 1.a even 1 1 trivial
833.2.l.e yes 40 17.d even 8 1 inner
833.2.v.g 80 7.c even 3 2
833.2.v.g 80 119.q even 24 2
833.2.v.h 80 7.d odd 6 2
833.2.v.h 80 119.r odd 24 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S2new(833,[χ])S_{2}^{\mathrm{new}}(833, [\chi]):

T240+168T236+16T233+10824T232+192T231+1056T229+⋯+2209 T_{2}^{40} + 168 T_{2}^{36} + 16 T_{2}^{33} + 10824 T_{2}^{32} + 192 T_{2}^{31} + 1056 T_{2}^{29} + \cdots + 2209 Copy content Toggle raw display
T340−4T339+8T338−32T336−4T335+328T334−1220T333+⋯+541696 T_{3}^{40} - 4 T_{3}^{39} + 8 T_{3}^{38} - 32 T_{3}^{36} - 4 T_{3}^{35} + 328 T_{3}^{34} - 1220 T_{3}^{33} + \cdots + 541696 Copy content Toggle raw display