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Properties

Label 833.2.r.a
Level $833$
Weight $2$
Character orbit 833.r
Analytic conductor $6.652$
Analytic rank $0$
Dimension $492$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(169,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([8, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.r (of order \(14\), degree \(6\), 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: \(492\)
Relative dimension: \(82\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 492 q - 10 q^{2} - 90 q^{4} - 2 q^{8} + 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 492 q - 10 q^{2} - 90 q^{4} - 2 q^{8} + 68 q^{9} - 6 q^{13} - 10 q^{15} - 94 q^{16} - 2 q^{17} - 40 q^{18} + 24 q^{19} - 14 q^{21} + 68 q^{25} - 26 q^{26} - 40 q^{30} + 14 q^{32} + 6 q^{33} + 15 q^{34} - 22 q^{35} + 46 q^{36} - 10 q^{38} + 28 q^{42} - 38 q^{43} + 56 q^{47} - 60 q^{49} - 28 q^{50} + 11 q^{51} + 50 q^{52} - 32 q^{53} + 68 q^{55} - 98 q^{59} - 22 q^{60} + 26 q^{64} - 86 q^{66} - 52 q^{67} + 8 q^{68} - 126 q^{69} - 18 q^{70} - 62 q^{72} - 58 q^{76} - 14 q^{77} - 108 q^{81} + 82 q^{83} - 206 q^{84} - 49 q^{85} - 56 q^{86} + 38 q^{87} + 32 q^{89} + 34 q^{93} - 162 q^{94} - 144 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
169.1 −2.47274 + 1.19081i −0.0878859 − 0.0200594i 3.44944 − 4.32547i −0.946628 − 0.216062i 0.241206 − 0.0550537i −1.89811 − 1.84314i −2.15734 + 9.45194i −2.69559 − 1.29813i 2.59805 − 0.592989i
169.2 −2.47274 + 1.19081i 0.0878859 + 0.0200594i 3.44944 − 4.32547i 0.946628 + 0.216062i −0.241206 + 0.0550537i 1.89811 + 1.84314i −2.15734 + 9.45194i −2.69559 − 1.29813i −2.59805 + 0.592989i
169.3 −2.40231 + 1.15689i −2.76669 − 0.631478i 3.18573 − 3.99478i 3.40724 + 0.777681i 7.37700 − 1.68375i 1.43423 − 2.22328i −1.84495 + 8.08324i 4.55288 + 2.19255i −9.08497 + 2.07358i
169.4 −2.40231 + 1.15689i 2.76669 + 0.631478i 3.18573 − 3.99478i −3.40724 − 0.777681i −7.37700 + 1.68375i −1.43423 + 2.22328i −1.84495 + 8.08324i 4.55288 + 2.19255i 9.08497 − 2.07358i
169.5 −2.26786 + 1.09214i −2.43385 − 0.555510i 2.70343 − 3.38999i −2.66117 − 0.607395i 6.12633 − 1.39829i 1.86815 − 1.87351i −1.30841 + 5.73252i 2.91213 + 1.40241i 6.69852 − 1.52889i
169.6 −2.26786 + 1.09214i 2.43385 + 0.555510i 2.70343 − 3.38999i 2.66117 + 0.607395i −6.12633 + 1.39829i −1.86815 + 1.87351i −1.30841 + 5.73252i 2.91213 + 1.40241i −6.69852 + 1.52889i
169.7 −2.21738 + 1.06784i −2.17087 − 0.495487i 2.52954 − 3.17194i −0.524303 − 0.119669i 5.34275 − 1.21945i −2.60210 − 0.478595i −1.12655 + 4.93573i 1.76427 + 0.849627i 1.29037 − 0.294518i
169.8 −2.21738 + 1.06784i 2.17087 + 0.495487i 2.52954 − 3.17194i 0.524303 + 0.119669i −5.34275 + 1.21945i 2.60210 + 0.478595i −1.12655 + 4.93573i 1.76427 + 0.849627i −1.29037 + 0.294518i
169.9 −2.17309 + 1.04650i −0.879703 − 0.200787i 2.38017 − 2.98463i −3.90116 − 0.890415i 2.12180 − 0.484287i 0.750520 + 2.53707i −0.975462 + 4.27378i −1.96934 − 0.948386i 9.40940 − 2.14763i
169.10 −2.17309 + 1.04650i 0.879703 + 0.200787i 2.38017 − 2.98463i 3.90116 + 0.890415i −2.12180 + 0.484287i −0.750520 − 2.53707i −0.975462 + 4.27378i −1.96934 − 0.948386i −9.40940 + 2.14763i
169.11 −1.97610 + 0.951641i −2.11926 − 0.483707i 1.75239 − 2.19742i 0.422065 + 0.0963336i 4.64819 − 1.06092i 1.47360 + 2.19739i −0.395623 + 1.73334i 1.55438 + 0.748550i −0.925720 + 0.211289i
169.12 −1.97610 + 0.951641i 2.11926 + 0.483707i 1.75239 − 2.19742i −0.422065 − 0.0963336i −4.64819 + 1.06092i −1.47360 − 2.19739i −0.395623 + 1.73334i 1.55438 + 0.748550i 0.925720 − 0.211289i
169.13 −1.87504 + 0.902971i −0.173477 − 0.0395951i 1.45344 − 1.82255i 0.445134 + 0.101599i 0.361030 − 0.0824027i 2.22262 − 1.43525i −0.153345 + 0.671848i −2.67438 − 1.28791i −0.926384 + 0.211441i
169.14 −1.87504 + 0.902971i 0.173477 + 0.0395951i 1.45344 − 1.82255i −0.445134 − 0.101599i −0.361030 + 0.0824027i −2.22262 + 1.43525i −0.153345 + 0.671848i −2.67438 − 1.28791i 0.926384 − 0.211441i
169.15 −1.77611 + 0.855330i −2.08341 − 0.475524i 1.17600 − 1.47466i 2.90506 + 0.663062i 4.10709 − 0.937417i −2.62829 + 0.303505i 0.0499380 − 0.218793i 1.41156 + 0.679772i −5.72685 + 1.30712i
169.16 −1.77611 + 0.855330i 2.08341 + 0.475524i 1.17600 − 1.47466i −2.90506 − 0.663062i −4.10709 + 0.937417i 2.62829 − 0.303505i 0.0499380 − 0.218793i 1.41156 + 0.679772i 5.72685 − 1.30712i
169.17 −1.61880 + 0.779575i −2.11346 − 0.482383i 0.765808 − 0.960292i −2.21731 − 0.506086i 3.79733 − 0.866715i −1.03541 − 2.43473i 0.308550 − 1.35185i 1.53110 + 0.737341i 3.98391 − 0.909302i
169.18 −1.61880 + 0.779575i 2.11346 + 0.482383i 0.765808 − 0.960292i 2.21731 + 0.506086i −3.79733 + 0.866715i 1.03541 + 2.43473i 0.308550 − 1.35185i 1.53110 + 0.737341i −3.98391 + 0.909302i
169.19 −1.45576 + 0.701059i −0.163540 − 0.0373268i 0.380785 − 0.477489i 4.24805 + 0.969589i 0.264243 − 0.0603118i 0.658706 + 2.56244i 0.499503 − 2.18847i −2.67755 − 1.28944i −6.86389 + 1.56664i
169.20 −1.45576 + 0.701059i 0.163540 + 0.0373268i 0.380785 − 0.477489i −4.24805 − 0.969589i −0.264243 + 0.0603118i −0.658706 − 2.56244i 0.499503 − 2.18847i −2.67755 − 1.28944i 6.86389 − 1.56664i
See next 80 embeddings (of 492 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 169.82
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.b even 2 1 inner
49.e even 7 1 inner
833.r even 14 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.r.a ✓ 492
17.b even 2 1 inner 833.2.r.a ✓ 492
49.e even 7 1 inner 833.2.r.a ✓ 492
833.r even 14 1 inner 833.2.r.a ✓ 492
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.r.a ✓ 492 1.a even 1 1 trivial
833.2.r.a ✓ 492 17.b even 2 1 inner
833.2.r.a ✓ 492 49.e even 7 1 inner
833.2.r.a ✓ 492 833.r even 14 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(833, [\chi])\).