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Properties

Label 8019.2.a.l
Level $8019$
Weight $2$
Character orbit 8019.a
Self dual yes
Analytic conductor $64.032$
Analytic rank $0$
Dimension $51$
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: \(51\)
Twist minimal: no (minimal twist has level 297)
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.

\(\operatorname{Tr}(f)(q) = \) \( 51 q + 60 q^{4} + 6 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 51 q + 60 q^{4} + 6 q^{5} + 12 q^{7} + 18 q^{10} + 51 q^{11} + 30 q^{13} + 12 q^{14} + 78 q^{16} + 30 q^{19} + 18 q^{20} + 3 q^{23} + 75 q^{25} + 9 q^{26} + 36 q^{28} + 42 q^{31} - 15 q^{32} + 42 q^{34} - 9 q^{35} + 48 q^{37} - 3 q^{38} + 54 q^{40} + 18 q^{43} + 60 q^{44} + 42 q^{46} + 30 q^{47} + 99 q^{49} - 30 q^{50} + 60 q^{52} + 18 q^{53} + 6 q^{55} + 21 q^{56} + 30 q^{58} + 24 q^{59} + 99 q^{61} + 114 q^{64} - 15 q^{65} + 39 q^{67} - 39 q^{68} + 48 q^{70} + 30 q^{71} + 69 q^{73} + 90 q^{76} + 12 q^{77} + 48 q^{79} + 42 q^{80} + 42 q^{82} - 21 q^{83} + 84 q^{85} + 24 q^{86} + 15 q^{89} + 69 q^{91} - 66 q^{92} + 66 q^{94} - 12 q^{95} + 72 q^{97} - 57 q^{98}+O(q^{100}) \) 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 −2.79071 0 5.78806 −3.06614 0 −1.43628 −10.5714 0 8.55671
1.2 −2.71465 0 5.36931 3.09118 0 4.07222 −9.14647 0 −8.39147
1.3 −2.66034 0 5.07742 3.00650 0 −4.51333 −8.18698 0 −7.99831
1.4 −2.65065 0 5.02592 −0.556977 0 3.79141 −8.02065 0 1.47635
1.5 −2.49410 0 4.22054 −0.845382 0 2.75453 −5.53826 0 2.10847
1.6 −2.41765 0 3.84501 −4.26448 0 −1.48558 −4.46059 0 10.3100
1.7 −2.35184 0 3.53116 1.70161 0 −2.57467 −3.60105 0 −4.00192
1.8 −2.30721 0 3.32320 −3.68924 0 2.72959 −3.05291 0 8.51183
1.9 −1.98291 0 1.93194 0.594867 0 −1.24839 0.134957 0 −1.17957
1.10 −1.89185 0 1.57908 −1.88472 0 1.84735 0.796313 0 3.56560
1.11 −1.83739 0 1.37599 3.72662 0 0.891460 1.14655 0 −6.84725
1.12 −1.79315 0 1.21539 3.19791 0 −3.70301 1.40692 0 −5.73435
1.13 −1.65054 0 0.724279 1.45553 0 −4.69391 2.10563 0 −2.40240
1.14 −1.64539 0 0.707320 −1.78224 0 −2.05789 2.12697 0 2.93248
1.15 −1.44992 0 0.102274 1.93239 0 2.99081 2.75156 0 −2.80182
1.16 −1.44748 0 0.0951963 −3.47143 0 5.22882 2.75716 0 5.02482
1.17 −1.18428 0 −0.597486 2.95374 0 3.03845 3.07615 0 −3.49805
1.18 −1.08097 0 −0.831507 −2.81118 0 −2.10385 3.06077 0 3.03880
1.19 −0.933308 0 −1.12894 1.97519 0 5.04438 2.92026 0 −1.84346
1.20 −0.763545 0 −1.41700 −2.20032 0 −4.85667 2.60903 0 1.68004
See all 51 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.51
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.l 51
3.b odd 2 1 8019.2.a.k 51
27.e even 9 2 297.2.j.c ✓ 102
27.f odd 18 2 891.2.j.c 102
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
297.2.j.c ✓ 102 27.e even 9 2
891.2.j.c 102 27.f odd 18 2
8019.2.a.k 51 3.b odd 2 1
8019.2.a.l 51 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{51} - 81 T_{2}^{49} + 3069 T_{2}^{47} + 3 T_{2}^{46} - 72291 T_{2}^{45} - 213 T_{2}^{44} + \cdots - 576 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\). Copy content Toggle raw display