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Properties

Label 833.2.l.g
Level $833$
Weight $2$
Character orbit 833.l
Analytic conductor $6.652$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(246,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.l (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 119)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{2} + 4 q^{3} - 8 q^{6} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{2} + 4 q^{3} - 8 q^{6} - 16 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 28 q^{12} + 12 q^{15} - 8 q^{16} - 4 q^{17} + 24 q^{18} + 4 q^{19} - 24 q^{20} - 24 q^{22} - 8 q^{23} + 28 q^{24} + 8 q^{25} - 36 q^{26} - 32 q^{27} - 8 q^{29} + 4 q^{31} - 48 q^{32} - 40 q^{33} - 8 q^{34} - 16 q^{36} + 36 q^{37} - 16 q^{39} - 28 q^{40} + 20 q^{41} + 8 q^{43} + 20 q^{44} - 8 q^{45} + 4 q^{46} + 28 q^{48} + 8 q^{50} - 44 q^{51} + 24 q^{52} + 20 q^{53} - 24 q^{54} - 8 q^{57} - 28 q^{58} - 4 q^{59} - 76 q^{60} + 24 q^{61} + 44 q^{62} - 8 q^{65} - 12 q^{66} + 60 q^{68} + 96 q^{69} - 16 q^{71} + 24 q^{73} + 28 q^{74} + 108 q^{75} - 4 q^{76} + 80 q^{78} + 4 q^{79} + 44 q^{80} - 24 q^{82} - 44 q^{83} - 20 q^{85} - 64 q^{86} - 68 q^{87} - 104 q^{88} - 24 q^{90} - 40 q^{92} - 8 q^{93} - 44 q^{94} - 48 q^{95} + 12 q^{96} + 40 q^{97} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
246.1 −1.65959 + 1.65959i −0.945255 + 2.28205i − 3.50846i 0.904040 + 0.374466i −2.21852 − 5.35599i 0 2.50343 + 2.50343i −2.19291 − 2.19291i −2.12179 + 0.878876i
246.2 −1.37277 + 1.37277i −0.181346 + 0.437807i − 1.76897i −3.14575 − 1.30301i −0.352062 − 0.849952i 0 −0.317147 − 0.317147i 1.96253 + 1.96253i 6.10711 − 2.52965i
246.3 −1.12386 + 1.12386i 0.860453 − 2.07732i − 0.526128i 2.47826 + 1.02653i 1.36759 + 3.30165i 0 −1.65643 − 1.65643i −1.45355 − 1.45355i −3.93890 + 1.63154i
246.4 −0.345355 + 0.345355i −0.799043 + 1.92906i 1.76146i 0.946188 + 0.391924i −0.390257 − 0.942164i 0 −1.29904 − 1.29904i −0.961484 − 0.961484i −0.462124 + 0.191418i
246.5 −0.0570754 + 0.0570754i −0.232516 + 0.561344i 1.99348i 1.68645 + 0.698551i −0.0187680 − 0.0453099i 0 −0.227930 − 0.227930i 1.86028 + 1.86028i −0.136125 + 0.0563848i
246.6 0.176571 − 0.176571i 1.22468 − 2.95665i 1.93765i −2.05102 − 0.849558i −0.305815 − 0.738304i 0 0.695276 + 0.695276i −5.12060 − 5.12060i −0.512158 + 0.212143i
246.7 0.768548 − 0.768548i 0.0886661 − 0.214059i 0.818669i −3.21867 − 1.33322i −0.0963703 − 0.232659i 0 2.16628 + 2.16628i 2.08336 + 2.08336i −3.49834 + 1.44906i
246.8 1.32279 − 1.32279i −0.00695315 + 0.0167864i − 1.49952i 0.519209 + 0.215064i 0.0130073 + 0.0314023i 0 0.662025 + 0.662025i 2.12109 + 2.12109i 0.971285 − 0.402320i
246.9 1.33748 − 1.33748i 0.902864 − 2.17971i − 1.57768i 3.13143 + 1.29708i −1.70775 − 4.12286i 0 0.564839 + 0.564839i −1.81464 − 1.81464i 5.92302 − 2.45340i
246.10 1.95327 − 1.95327i −0.618661 + 1.49358i − 5.63049i −1.25014 − 0.517825i 1.70895 + 4.12577i 0 −7.09131 − 7.09131i 0.273282 + 0.273282i −3.45330 + 1.43041i
393.1 −1.66289 − 1.66289i 1.63644 − 0.677836i 3.53038i 0.205704 + 0.496614i −3.84838 − 1.59405i 0 2.54485 − 2.54485i 0.0971540 − 0.0971540i 0.483750 − 1.16788i
393.2 −1.28230 − 1.28230i −1.55166 + 0.642719i 1.28858i 1.40079 + 3.38180i 2.81385 + 1.16554i 0 −0.912255 + 0.912255i −0.126755 + 0.126755i 2.54025 − 6.13271i
393.3 −1.07383 − 1.07383i −0.882931 + 0.365722i 0.306209i −0.477398 − 1.15254i 1.34084 + 0.555393i 0 −1.81884 + 1.81884i −1.47551 + 1.47551i −0.724987 + 1.75027i
393.4 −0.574435 − 0.574435i 2.83040 − 1.17239i − 1.34005i 0.724358 + 1.74876i −2.29934 − 0.952418i 0 −1.91864 + 1.91864i 4.51533 − 4.51533i 0.588449 − 1.42064i
393.5 −0.218704 − 0.218704i 0.530328 − 0.219669i − 1.90434i −1.41235 − 3.40971i −0.164028 − 0.0679424i 0 −0.853895 + 0.853895i −1.88833 + 1.88833i −0.436831 + 1.05460i
393.6 0.309239 + 0.309239i −2.18534 + 0.905196i − 1.80874i 0.192697 + 0.465212i −0.955714 − 0.395870i 0 1.17781 − 1.17781i 1.83500 − 1.83500i −0.0842723 + 0.203451i
393.7 1.09621 + 1.09621i 0.791288 − 0.327762i 0.403368i 0.252972 + 0.610729i 1.22672 + 0.508123i 0 1.75025 − 1.75025i −1.60261 + 1.60261i −0.392178 + 0.946802i
393.8 1.10720 + 1.10720i 2.70809 − 1.12173i 0.451767i −0.392048 − 0.946488i 4.24036 + 1.75642i 0 1.71420 − 1.71420i 3.95416 − 3.95416i 0.613874 − 1.48202i
393.9 1.43405 + 1.43405i −2.24417 + 0.929567i 2.11297i −1.26519 − 3.05445i −4.55129 − 1.88520i 0 −0.162010 + 0.162010i 2.05090 − 2.05090i 2.56587 − 6.19456i
393.10 1.86546 + 1.86546i 0.0746649 − 0.0309272i 4.95985i 0.770466 + 1.86007i 0.196977 + 0.0815907i 0 −5.52147 + 5.52147i −2.11670 + 2.11670i −2.03261 + 4.90715i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 246.10
Significant digits:
Format:

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.g 40
7.b odd 2 1 833.2.l.f 40
7.c even 3 2 119.2.q.a ✓ 80
7.d odd 6 2 833.2.v.f 80
17.d even 8 1 inner 833.2.l.g 40
119.l odd 8 1 833.2.l.f 40
119.q even 24 2 119.2.q.a ✓ 80
119.r odd 24 2 833.2.v.f 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.2.q.a ✓ 80 7.c even 3 2
119.2.q.a ✓ 80 119.q even 24 2
833.2.l.f 40 7.b odd 2 1
833.2.l.f 40 119.l odd 8 1
833.2.l.g 40 1.a even 1 1 trivial
833.2.l.g 40 17.d even 8 1 inner
833.2.v.f 80 7.d odd 6 2
833.2.v.f 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 \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{40} - 4 T_{2}^{39} + 8 T_{2}^{38} + 98 T_{2}^{36} - 392 T_{2}^{35} + 784 T_{2}^{34} - 4 T_{2}^{33} + \cdots + 49 \) Copy content Toggle raw display
\( T_{3}^{40} - 4 T_{3}^{39} + 6 T_{3}^{38} + 8 T_{3}^{37} - 46 T_{3}^{36} + 348 T_{3}^{34} + 432 T_{3}^{33} + \cdots + 1 \) Copy content Toggle raw display