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Properties

Label 833.2.l.b
Level $833$
Weight $2$
Character orbit 833.l
Analytic conductor $6.652$
Analytic rank $0$
Dimension $32$
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(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: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 24 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 24 q^{18} + 8 q^{23} + 8 q^{25} - 16 q^{29} - 40 q^{32} - 8 q^{36} - 8 q^{37} + 8 q^{39} - 24 q^{43} + 64 q^{44} - 80 q^{46} + 16 q^{50} + 8 q^{51} + 32 q^{53} - 8 q^{57} - 104 q^{58} + 152 q^{60} - 64 q^{65} + 96 q^{67} - 48 q^{71} - 24 q^{74} - 136 q^{78} - 80 q^{79} + 72 q^{85} - 72 q^{86} + 56 q^{88} + 8 q^{92} - 48 q^{93} - 32 q^{95} + 8 q^{99}+O(q^{100}) \) 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 −1.61504 + 1.61504i −0.678714 + 1.63856i − 3.21670i 1.74157 + 0.721382i −1.55019 − 3.74249i 0 1.96501 + 1.96501i −0.102907 − 0.102907i −3.97776 + 1.64764i
246.2 −1.61504 + 1.61504i 0.678714 − 1.63856i − 3.21670i −1.74157 − 0.721382i 1.55019 + 3.74249i 0 1.96501 + 1.96501i −0.102907 − 0.102907i 3.97776 − 1.64764i
246.3 −0.410438 + 0.410438i −0.115059 + 0.277778i 1.66308i 2.34406 + 0.970942i −0.0667860 − 0.161236i 0 −1.50347 − 1.50347i 2.05740 + 2.05740i −1.36061 + 0.563581i
246.4 −0.410438 + 0.410438i 0.115059 − 0.277778i 1.66308i −2.34406 − 0.970942i 0.0667860 + 0.161236i 0 −1.50347 − 1.50347i 2.05740 + 2.05740i 1.36061 − 0.563581i
246.5 0.916903 − 0.916903i −0.753114 + 1.81818i 0.318579i −1.26053 − 0.522128i 0.976561 + 2.35763i 0 2.12591 + 2.12591i −0.617274 − 0.617274i −1.63452 + 0.677041i
246.6 0.916903 − 0.916903i 0.753114 − 1.81818i 0.318579i 1.26053 + 0.522128i −0.976561 − 2.35763i 0 2.12591 + 2.12591i −0.617274 − 0.617274i 1.63452 − 0.677041i
246.7 1.81568 − 1.81568i −0.622784 + 1.50353i − 4.59339i 3.40232 + 1.40929i 1.59916 + 3.86071i 0 −4.70877 − 4.70877i 0.248569 + 0.248569i 8.73634 − 3.61871i
246.8 1.81568 − 1.81568i 0.622784 − 1.50353i − 4.59339i −3.40232 − 1.40929i −1.59916 − 3.86071i 0 −4.70877 − 4.70877i 0.248569 + 0.248569i −8.73634 + 3.61871i
393.1 −1.52898 − 1.52898i −2.34631 + 0.971874i 2.67554i −0.0142930 − 0.0345063i 5.07343 + 2.10148i 0 1.03289 − 1.03289i 2.43932 − 2.43932i −0.0309057 + 0.0746129i
393.2 −1.52898 − 1.52898i 2.34631 − 0.971874i 2.67554i 0.0142930 + 0.0345063i −5.07343 − 2.10148i 0 1.03289 − 1.03289i 2.43932 − 2.43932i 0.0309057 − 0.0746129i
393.3 −0.642126 − 0.642126i −0.912963 + 0.378162i − 1.17535i 0.851760 + 2.05633i 0.829065 + 0.343410i 0 −2.03897 + 2.03897i −1.43083 + 1.43083i 0.773487 − 1.86736i
393.4 −0.642126 − 0.642126i 0.912963 − 0.378162i − 1.17535i −0.851760 − 2.05633i −0.829065 − 0.343410i 0 −2.03897 + 2.03897i −1.43083 + 1.43083i −0.773487 + 1.86736i
393.5 0.368647 + 0.368647i −2.78465 + 1.15344i − 1.72820i −1.27589 − 3.08026i −1.45177 − 0.601342i 0 1.37439 − 1.37439i 4.30254 − 4.30254i 0.665179 − 1.60588i
393.6 0.368647 + 0.368647i 2.78465 − 1.15344i − 1.72820i 1.27589 + 3.08026i 1.45177 + 0.601342i 0 1.37439 − 1.37439i 4.30254 − 4.30254i −0.665179 + 1.60588i
393.7 1.09535 + 1.09535i −1.21577 + 0.503589i 0.399579i 0.976741 + 2.35806i −1.88330 − 0.780088i 0 1.75302 − 1.75302i −0.896823 + 0.896823i −1.51303 + 3.65277i
393.8 1.09535 + 1.09535i 1.21577 − 0.503589i 0.399579i −0.976741 − 2.35806i 1.88330 + 0.780088i 0 1.75302 − 1.75302i −0.896823 + 0.896823i 1.51303 − 3.65277i
491.1 −1.61504 − 1.61504i −0.678714 − 1.63856i 3.21670i 1.74157 − 0.721382i −1.55019 + 3.74249i 0 1.96501 − 1.96501i −0.102907 + 0.102907i −3.97776 − 1.64764i
491.2 −1.61504 − 1.61504i 0.678714 + 1.63856i 3.21670i −1.74157 + 0.721382i 1.55019 − 3.74249i 0 1.96501 − 1.96501i −0.102907 + 0.102907i 3.97776 + 1.64764i
491.3 −0.410438 − 0.410438i −0.115059 − 0.277778i − 1.66308i 2.34406 − 0.970942i −0.0667860 + 0.161236i 0 −1.50347 + 1.50347i 2.05740 − 2.05740i −1.36061 − 0.563581i
491.4 −0.410438 − 0.410438i 0.115059 + 0.277778i − 1.66308i −2.34406 + 0.970942i 0.0667860 − 0.161236i 0 −1.50347 + 1.50347i 2.05740 − 2.05740i 1.36061 + 0.563581i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 246.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
17.d even 8 1 inner
119.l odd 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.b ✓ 32
7.b odd 2 1 inner 833.2.l.b ✓ 32
7.c even 3 2 833.2.v.d 64
7.d odd 6 2 833.2.v.d 64
17.d even 8 1 inner 833.2.l.b ✓ 32
119.l odd 8 1 inner 833.2.l.b ✓ 32
119.q even 24 2 833.2.v.d 64
119.r odd 24 2 833.2.v.d 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.l.b ✓ 32 1.a even 1 1 trivial
833.2.l.b ✓ 32 7.b odd 2 1 inner
833.2.l.b ✓ 32 17.d even 8 1 inner
833.2.l.b ✓ 32 119.l odd 8 1 inner
833.2.v.d 64 7.c even 3 2
833.2.v.d 64 7.d odd 6 2
833.2.v.d 64 119.q even 24 2
833.2.v.d 64 119.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 \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{16} + 51 T_{2}^{12} + 4 T_{2}^{11} - 44 T_{2}^{9} + 513 T_{2}^{8} - 140 T_{2}^{7} + 8 T_{2}^{6} + \cdots + 49 \) Copy content Toggle raw display
\( T_{3}^{32} - 12 T_{3}^{30} + 72 T_{3}^{28} + 144 T_{3}^{26} + 142 T_{3}^{24} - 4220 T_{3}^{22} + \cdots + 83521 \) Copy content Toggle raw display