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Properties

Label 833.2.v.d
Level $833$
Weight $2$
Character orbit 833.v
Analytic conductor $6.652$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(128,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.128");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.v (of order \(24\), degree \(8\), not 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: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q - 24 q^{9} - 8 q^{11} - 16 q^{15} + 8 q^{16} + 24 q^{18} - 8 q^{23} - 8 q^{25} - 32 q^{29} + 40 q^{32} - 16 q^{36} + 8 q^{37} - 8 q^{39} - 48 q^{43} - 64 q^{44} + 80 q^{46} + 32 q^{50} - 8 q^{51} - 32 q^{53} - 16 q^{57} + 104 q^{58} - 152 q^{60} + 64 q^{65} - 96 q^{67} - 96 q^{71} + 24 q^{74} - 272 q^{78} + 80 q^{79} + 144 q^{85} + 72 q^{86} - 56 q^{88} + 16 q^{92} + 48 q^{93} + 32 q^{95} + 16 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
128.1 −0.559644 − 2.08862i −0.331488 − 2.51790i −2.31709 + 1.33777i 0.0227368 + 0.0296312i −5.07343 + 2.10148i 0 1.03289 + 1.03289i −3.33217 + 0.892853i 0.0491638 − 0.0640716i
128.2 −0.559644 − 2.08862i 0.331488 + 2.51790i −2.31709 + 1.33777i −0.0227368 − 0.0296312i 5.07343 − 2.10148i 0 1.03289 + 1.03289i −3.33217 + 0.892853i −0.0491638 + 0.0640716i
128.3 −0.235035 − 0.877161i −0.128984 − 0.979730i 1.01788 − 0.587674i −1.35496 − 1.76581i −0.829065 + 0.343410i 0 −2.03897 − 2.03897i 1.95454 − 0.523718i −1.23044 + 1.60354i
128.4 −0.235035 − 0.877161i 0.128984 + 0.979730i 1.01788 − 0.587674i 1.35496 + 1.76581i 0.829065 − 0.343410i 0 −2.03897 − 2.03897i 1.95454 − 0.523718i 1.23044 − 1.60354i
128.5 0.134934 + 0.503581i −0.393417 − 2.98830i 1.49666 − 0.864099i 2.02964 + 2.64508i 1.45177 − 0.601342i 0 1.37439 + 1.37439i −5.87738 + 1.57484i −1.05815 + 1.37900i
128.6 0.134934 + 0.503581i 0.393417 + 2.98830i 1.49666 − 0.864099i −2.02964 − 2.64508i −1.45177 + 0.601342i 0 1.37439 + 1.37439i −5.87738 + 1.57484i 1.05815 − 1.37900i
128.7 0.400926 + 1.49627i −0.171765 − 1.30468i −0.346046 + 0.199790i −1.55377 − 2.02491i 1.88330 − 0.780088i 0 1.75302 + 1.75302i 1.22508 − 0.328260i 2.40688 − 3.13671i
128.8 0.400926 + 1.49627i 0.171765 + 1.30468i −0.346046 + 0.199790i 1.55377 + 2.02491i −1.88330 + 0.780088i 0 1.75302 + 1.75302i 1.22508 − 0.328260i −2.40688 + 3.13671i
263.1 −2.48027 − 0.664585i −0.990706 − 1.29111i 3.97799 + 2.29670i −0.480681 − 3.65114i 1.59916 + 3.86071i 0 −4.70877 − 4.70877i 0.0909827 − 0.339552i −1.23427 + 9.37524i
263.2 −2.48027 − 0.664585i 0.990706 + 1.29111i 3.97799 + 2.29670i 0.480681 + 3.65114i −1.59916 − 3.86071i 0 −4.70877 − 4.70877i 0.0909827 − 0.339552i 1.23427 − 9.37524i
263.3 −1.25251 − 0.335610i −1.19803 − 1.56131i −0.275898 − 0.159290i 0.178088 + 1.35271i 0.976561 + 2.35763i 0 2.12591 + 2.12591i −0.225938 + 0.843212i 0.230926 − 1.75406i
263.4 −1.25251 − 0.335610i 1.19803 + 1.56131i −0.275898 − 0.159290i −0.178088 − 1.35271i −0.976561 − 2.35763i 0 2.12591 + 2.12591i −0.225938 + 0.843212i −0.230926 + 1.75406i
263.5 0.560669 + 0.150231i −0.183033 − 0.238534i −1.44027 − 0.831540i −0.331170 − 2.51549i −0.0667860 − 0.161236i 0 −1.50347 − 1.50347i 0.753060 − 2.81046i 0.192227 − 1.46011i
263.6 0.560669 + 0.150231i 0.183033 + 0.238534i −1.44027 − 0.831540i 0.331170 + 2.51549i 0.0667860 + 0.161236i 0 −1.50347 − 1.50347i 0.753060 − 2.81046i −0.192227 + 1.46011i
263.7 2.20618 + 0.591145i −1.07968 − 1.40706i 2.78574 + 1.60835i −0.246050 − 1.86893i −1.55019 − 3.74249i 0 1.96501 + 1.96501i −0.0376667 + 0.140574i 0.561980 − 4.26866i
263.8 2.20618 + 0.591145i 1.07968 + 1.40706i 2.78574 + 1.60835i 0.246050 + 1.86893i 1.55019 + 3.74249i 0 1.96501 + 1.96501i −0.0376667 + 0.140574i −0.561980 + 4.26866i
410.1 −0.559644 + 2.08862i −0.331488 + 2.51790i −2.31709 − 1.33777i 0.0227368 − 0.0296312i −5.07343 − 2.10148i 0 1.03289 − 1.03289i −3.33217 − 0.892853i 0.0491638 + 0.0640716i
410.2 −0.559644 + 2.08862i 0.331488 − 2.51790i −2.31709 − 1.33777i −0.0227368 + 0.0296312i 5.07343 + 2.10148i 0 1.03289 − 1.03289i −3.33217 − 0.892853i −0.0491638 − 0.0640716i
410.3 −0.235035 + 0.877161i −0.128984 + 0.979730i 1.01788 + 0.587674i −1.35496 + 1.76581i −0.829065 − 0.343410i 0 −2.03897 + 2.03897i 1.95454 + 0.523718i −1.23044 − 1.60354i
410.4 −0.235035 + 0.877161i 0.128984 − 0.979730i 1.01788 + 0.587674i 1.35496 − 1.76581i 0.829065 + 0.343410i 0 −2.03897 + 2.03897i 1.95454 + 0.523718i 1.23044 + 1.60354i
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 128.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
7.c even 3 1 inner
7.d odd 6 1 inner
17.d even 8 1 inner
119.l odd 8 1 inner
119.q even 24 1 inner
119.r odd 24 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.v.d 64
7.b odd 2 1 inner 833.2.v.d 64
7.c even 3 1 833.2.l.b ✓ 32
7.c even 3 1 inner 833.2.v.d 64
7.d odd 6 1 833.2.l.b ✓ 32
7.d odd 6 1 inner 833.2.v.d 64
17.d even 8 1 inner 833.2.v.d 64
119.l odd 8 1 inner 833.2.v.d 64
119.q even 24 1 833.2.l.b ✓ 32
119.q even 24 1 inner 833.2.v.d 64
119.r odd 24 1 833.2.l.b ✓ 32
119.r odd 24 1 inner 833.2.v.d 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.l.b ✓ 32 7.c even 3 1
833.2.l.b ✓ 32 7.d odd 6 1
833.2.l.b ✓ 32 119.q even 24 1
833.2.l.b ✓ 32 119.r odd 24 1
833.2.v.d 64 1.a even 1 1 trivial
833.2.v.d 64 7.b odd 2 1 inner
833.2.v.d 64 7.c even 3 1 inner
833.2.v.d 64 7.d odd 6 1 inner
833.2.v.d 64 17.d even 8 1 inner
833.2.v.d 64 119.l odd 8 1 inner
833.2.v.d 64 119.q even 24 1 inner
833.2.v.d 64 119.r odd 24 1 inner

Hecke kernels

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

\( T_{2}^{32} - 51 T_{2}^{28} - 4 T_{2}^{27} + 44 T_{2}^{25} + 2088 T_{2}^{24} - 484 T_{2}^{23} + \cdots + 2401 \) Copy content Toggle raw display
\( T_{3}^{64} + 12 T_{3}^{62} + 72 T_{3}^{60} + 1152 T_{3}^{58} + 6770 T_{3}^{56} - 9556 T_{3}^{54} + \cdots + 6975757441 \) Copy content Toggle raw display