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Properties

Label 8019.2.a.j
Level $8019$
Weight $2$
Character orbit 8019.a
Self dual yes
Analytic conductor $64.032$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8019,2,Mod(1,8019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8019, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8019 = 3^{6} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8019.a (trivial)

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: yes
Analytic conductor: \(64.0320373809\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 6 q^{2} + 54 q^{4} + 24 q^{5} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 6 q^{2} + 54 q^{4} + 24 q^{5} + 18 q^{8} + 48 q^{11} + 24 q^{14} + 66 q^{16} + 24 q^{17} + 48 q^{20} + 6 q^{22} + 12 q^{23} + 60 q^{25} + 36 q^{26} - 18 q^{28} + 60 q^{29} + 36 q^{31} + 42 q^{32} + 12 q^{34} + 24 q^{35} + 6 q^{37} + 24 q^{38} + 72 q^{41} - 12 q^{43} + 54 q^{44} - 30 q^{46} + 36 q^{47} + 60 q^{49} + 42 q^{50} + 48 q^{53} + 24 q^{55} + 72 q^{56} + 12 q^{58} + 60 q^{59} - 24 q^{61} + 36 q^{62} + 90 q^{64} + 48 q^{65} + 60 q^{68} - 30 q^{70} + 60 q^{71} - 18 q^{73} + 36 q^{74} - 42 q^{76} - 12 q^{79} + 96 q^{80} + 12 q^{82} + 36 q^{83} + 18 q^{85} + 48 q^{86} + 18 q^{88} + 96 q^{89} + 30 q^{91} + 36 q^{92} - 48 q^{94} + 48 q^{95} + 30 q^{97} + 54 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.73086 0 5.45757 1.64852 0 −3.68547 −9.44213 0 −4.50188
1.2 −2.69860 0 5.28242 2.77916 0 1.18819 −8.85793 0 −7.49984
1.3 −2.64336 0 4.98736 −0.579709 0 −5.09157 −7.89669 0 1.53238
1.4 −2.34930 0 3.51919 1.75943 0 1.88450 −3.56903 0 −4.13341
1.5 −2.23656 0 3.00218 4.38914 0 0.803046 −2.24143 0 −9.81655
1.6 −2.15255 0 2.63345 −1.19810 0 −1.45395 −1.36354 0 2.57896
1.7 −2.14227 0 2.58933 −2.67313 0 −2.29738 −1.26251 0 5.72658
1.8 −2.08562 0 2.34981 −0.447082 0 −1.20128 −0.729568 0 0.932442
1.9 −1.97543 0 1.90232 3.33683 0 4.50897 0.192965 0 −6.59167
1.10 −1.89218 0 1.58034 −0.136704 0 2.04773 0.794073 0 0.258669
1.11 −1.83838 0 1.37966 −3.02957 0 0.342477 1.14043 0 5.56951
1.12 −1.63183 0 0.662854 −1.99029 0 0.560680 2.18199 0 3.24781
1.13 −1.30972 0 −0.284633 1.60231 0 −1.84969 2.99223 0 −2.09858
1.14 −1.25157 0 −0.433575 0.278672 0 0.0619923 3.04579 0 −0.348777
1.15 −1.23127 0 −0.483962 3.95179 0 −4.25016 3.05844 0 −4.86575
1.16 −0.897369 0 −1.19473 −3.26096 0 −3.00705 2.86685 0 2.92628
1.17 −0.885661 0 −1.21560 2.43396 0 4.39566 2.84794 0 −2.15567
1.18 −0.827541 0 −1.31518 −0.821063 0 3.85408 2.74344 0 0.679463
1.19 −0.613467 0 −1.62366 3.33683 0 1.90033 2.22300 0 −2.04704
1.20 −0.337235 0 −1.88627 0.914914 0 2.15702 1.31059 0 −0.308541
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.48
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(11\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8019.2.a.j yes 48
3.b odd 2 1 8019.2.a.i ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8019.2.a.i ✓ 48 3.b odd 2 1
8019.2.a.j yes 48 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{48} - 6 T_{2}^{47} - 57 T_{2}^{46} + 400 T_{2}^{45} + 1407 T_{2}^{44} - 12342 T_{2}^{43} + \cdots + 6813 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\). Copy content Toggle raw display