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Properties

Label 1083.2.d.d
Level $1083$
Weight $2$
Character orbit 1083.d
Analytic conductor $8.648$
Analytic rank $0$
Dimension $24$
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] = [1083,2,Mod(1082,1083)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1083, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1083.1082");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1083.d (of order \(2\), degree \(1\), 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: \(8.64779853890\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 36 q^{4} + 12 q^{6} + 12 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 36 q^{4} + 12 q^{6} + 12 q^{7} + 18 q^{9} - 12 q^{16} + 72 q^{24} - 24 q^{25} + 24 q^{28} - 84 q^{30} + 36 q^{36} - 18 q^{42} - 84 q^{43} - 12 q^{45} - 12 q^{49} - 54 q^{54} - 60 q^{55} + 24 q^{58} + 24 q^{61} - 30 q^{63} - 36 q^{64} - 6 q^{66} + 72 q^{73} + 42 q^{81} + 12 q^{82} + 12 q^{85} - 30 q^{87} + 48 q^{93} - 18 q^{96} + 60 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1082.1 −2.58014 −1.45137 + 0.945272i 4.65712 − 1.56090i 3.74472 − 2.43893i −2.99375 −6.85573 1.21292 − 2.74387i 4.02735i
1082.2 −2.58014 −1.45137 − 0.945272i 4.65712 1.56090i 3.74472 + 2.43893i −2.99375 −6.85573 1.21292 + 2.74387i − 4.02735i
1082.3 −2.21939 −0.641853 − 1.60873i 2.92570 2.76947i 1.42452 + 3.57041i 3.41826 −2.05449 −2.17605 + 2.06514i − 6.14655i
1082.4 −2.21939 −0.641853 + 1.60873i 2.92570 − 2.76947i 1.42452 − 3.57041i 3.41826 −2.05449 −2.17605 − 2.06514i 6.14655i
1082.5 −1.95593 −1.66750 + 0.468457i 1.82568 − 0.494605i 3.26152 − 0.916271i 1.93946 0.340959 2.56110 − 1.56230i 0.967415i
1082.6 −1.95593 −1.66750 − 0.468457i 1.82568 0.494605i 3.26152 + 0.916271i 1.93946 0.340959 2.56110 + 1.56230i − 0.967415i
1082.7 −1.93762 1.72228 + 0.183702i 1.75436 − 3.20284i −3.33712 − 0.355944i 2.46166 0.475963 2.93251 + 0.632773i 6.20587i
1082.8 −1.93762 1.72228 − 0.183702i 1.75436 3.20284i −3.33712 + 0.355944i 2.46166 0.475963 2.93251 − 0.632773i − 6.20587i
1082.9 −0.973467 0.570927 + 1.63525i −1.05236 − 3.84962i −0.555779 − 1.59186i 0.939926 2.97137 −2.34808 + 1.86722i 3.74748i
1082.10 −0.973467 0.570927 − 1.63525i −1.05236 3.84962i −0.555779 + 1.59186i 0.939926 2.97137 −2.34808 − 1.86722i − 3.74748i
1082.11 −0.943137 1.63058 − 0.584119i −1.11049 − 0.755808i −1.53786 + 0.550904i −2.76555 2.93362 2.31761 − 1.90491i 0.712830i
1082.12 −0.943137 1.63058 + 0.584119i −1.11049 0.755808i −1.53786 − 0.550904i −2.76555 2.93362 2.31761 + 1.90491i − 0.712830i
1082.13 0.943137 −1.63058 + 0.584119i −1.11049 − 0.755808i −1.53786 + 0.550904i −2.76555 −2.93362 2.31761 − 1.90491i − 0.712830i
1082.14 0.943137 −1.63058 − 0.584119i −1.11049 0.755808i −1.53786 − 0.550904i −2.76555 −2.93362 2.31761 + 1.90491i 0.712830i
1082.15 0.973467 −0.570927 − 1.63525i −1.05236 − 3.84962i −0.555779 − 1.59186i 0.939926 −2.97137 −2.34808 + 1.86722i − 3.74748i
1082.16 0.973467 −0.570927 + 1.63525i −1.05236 3.84962i −0.555779 + 1.59186i 0.939926 −2.97137 −2.34808 − 1.86722i 3.74748i
1082.17 1.93762 −1.72228 − 0.183702i 1.75436 − 3.20284i −3.33712 − 0.355944i 2.46166 −0.475963 2.93251 + 0.632773i − 6.20587i
1082.18 1.93762 −1.72228 + 0.183702i 1.75436 3.20284i −3.33712 + 0.355944i 2.46166 −0.475963 2.93251 − 0.632773i 6.20587i
1082.19 1.95593 1.66750 − 0.468457i 1.82568 − 0.494605i 3.26152 − 0.916271i 1.93946 −0.340959 2.56110 − 1.56230i − 0.967415i
1082.20 1.95593 1.66750 + 0.468457i 1.82568 0.494605i 3.26152 + 0.916271i 1.93946 −0.340959 2.56110 + 1.56230i 0.967415i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1082.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
19.b odd 2 1 inner
57.d even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1083.2.d.d 24
3.b odd 2 1 inner 1083.2.d.d 24
19.b odd 2 1 inner 1083.2.d.d 24
19.e even 9 1 57.2.j.b ✓ 24
19.f odd 18 1 57.2.j.b ✓ 24
57.d even 2 1 inner 1083.2.d.d 24
57.j even 18 1 57.2.j.b ✓ 24
57.l odd 18 1 57.2.j.b ✓ 24
76.k even 18 1 912.2.cc.e 24
76.l odd 18 1 912.2.cc.e 24
228.u odd 18 1 912.2.cc.e 24
228.v even 18 1 912.2.cc.e 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
57.2.j.b ✓ 24 19.e even 9 1
57.2.j.b ✓ 24 19.f odd 18 1
57.2.j.b ✓ 24 57.j even 18 1
57.2.j.b ✓ 24 57.l odd 18 1
912.2.cc.e 24 76.k even 18 1
912.2.cc.e 24 76.l odd 18 1
912.2.cc.e 24 228.u odd 18 1
912.2.cc.e 24 228.v even 18 1
1083.2.d.d 24 1.a even 1 1 trivial
1083.2.d.d 24 3.b odd 2 1 inner
1083.2.d.d 24 19.b odd 2 1 inner
1083.2.d.d 24 57.d even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} - 21T_{2}^{10} + 171T_{2}^{8} - 679T_{2}^{6} + 1347T_{2}^{4} - 1215T_{2}^{2} + 397 \) acting on \(S_{2}^{\mathrm{new}}(1083, [\chi])\). Copy content Toggle raw display