Properties

Label 8019.2.a.c
Level $8019$
Weight $2$
Character orbit 8019.a
Self dual yes
Analytic conductor $64.032$
Analytic rank $1$
Dimension $21$
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: \(1\)
Dimension: \(21\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q - 6 q^{2} + 18 q^{4} - 12 q^{5} - 18 q^{8} + 15 q^{10} + 21 q^{11} + 3 q^{13} - 24 q^{14} + 12 q^{16} - 12 q^{17} - 12 q^{19} - 15 q^{20} - 6 q^{22} + 15 q^{25} - 15 q^{26} + 42 q^{28} - 27 q^{29} + 6 q^{31} - 42 q^{32} - 6 q^{34} - 42 q^{35} + 3 q^{37} - 27 q^{38} + 30 q^{40} - 24 q^{41} + 6 q^{43} + 18 q^{44} - 51 q^{46} - 24 q^{47} - 9 q^{49} + 3 q^{50} + 9 q^{52} - 12 q^{53} - 12 q^{55} - 45 q^{56} + 12 q^{58} - 12 q^{59} - 30 q^{61} - 9 q^{62} + 42 q^{64} + 18 q^{67} - 30 q^{68} + 21 q^{70} - 36 q^{71} - 39 q^{73} - 27 q^{76} + 27 q^{79} - 78 q^{80} + 63 q^{82} - 42 q^{83} + 36 q^{85} - 42 q^{86} - 18 q^{88} - 36 q^{89} - 21 q^{91} - 6 q^{92} + 42 q^{94} - 24 q^{95} + 24 q^{97} - 69 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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 −2.71214 0 5.35571 −3.79183 0 3.96597 −9.10116 0 10.2840
1.2 −2.64385 0 4.98995 −1.69587 0 0.416922 −7.90499 0 4.48364
1.3 −2.51933 0 4.34701 −0.0919030 0 4.54767 −5.91287 0 0.231534
1.4 −2.38894 0 3.70703 1.18459 0 −1.03676 −4.07800 0 −2.82991
1.5 −1.73645 0 1.01527 0.0241179 0 −4.08219 1.70994 0 −0.0418795
1.6 −1.57842 0 0.491400 −2.27349 0 2.42031 2.38120 0 3.58851
1.7 −1.40249 0 −0.0330274 1.97794 0 1.49830 2.85130 0 −2.77404
1.8 −1.38639 0 −0.0779333 2.26790 0 −0.965210 2.88082 0 −3.14419
1.9 −1.02284 0 −0.953805 −2.76466 0 −3.04869 3.02126 0 2.82779
1.10 −0.878744 0 −1.22781 −1.62071 0 2.93534 2.83642 0 1.42419
1.11 −0.563863 0 −1.68206 −4.27233 0 0.945321 2.07618 0 2.40901
1.12 0.0682043 0 −1.99535 −1.18434 0 −4.66035 −0.272500 0 −0.0807768
1.13 0.455991 0 −1.79207 3.13439 0 0.856728 −1.72915 0 1.42925
1.14 0.521281 0 −1.72827 −0.302159 0 0.215327 −1.94347 0 −0.157510
1.15 1.01172 0 −0.976420 −4.44905 0 2.99336 −3.01131 0 −4.50120
1.16 1.29986 0 −0.310353 2.12386 0 −3.41757 −3.00315 0 2.76073
1.17 1.33160 0 −0.226829 3.20854 0 −2.77782 −2.96526 0 4.27251
1.18 1.44357 0 0.0839057 −3.26538 0 −0.792935 −2.76602 0 −4.71382
1.19 2.07274 0 2.29625 −0.494134 0 −1.40906 0.614038 0 −1.02421
1.20 2.25922 0 3.10409 1.06996 0 −0.137444 2.49438 0 2.41727
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
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.c 21
3.b odd 2 1 8019.2.a.f yes 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8019.2.a.c 21 1.a even 1 1 trivial
8019.2.a.f yes 21 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{21} + 6 T_{2}^{20} - 12 T_{2}^{19} - 130 T_{2}^{18} - 24 T_{2}^{17} + 1146 T_{2}^{16} + 1083 T_{2}^{15} - 5307 T_{2}^{14} - 7305 T_{2}^{13} + 13936 T_{2}^{12} + 24021 T_{2}^{11} - 20871 T_{2}^{10} - 44302 T_{2}^{9} + 16746 T_{2}^{8} + \cdots + 53 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\). Copy content Toggle raw display