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Properties

Label 8019.2.a.f
Level $8019$
Weight $2$
Character orbit 8019.a
Self dual yes
Analytic conductor $64.032$
Analytic rank $0$
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: \(0\)
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

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 −2.36924 0 3.61332 0.785442 0 1.53278 −3.82234 0 −1.86090
1.2 −2.25922 0 3.10409 −1.06996 0 −0.137444 −2.49438 0 2.41727
1.3 −2.07274 0 2.29625 0.494134 0 −1.40906 −0.614038 0 −1.02421
1.4 −1.44357 0 0.0839057 3.26538 0 −0.792935 2.76602 0 −4.71382
1.5 −1.33160 0 −0.226829 −3.20854 0 −2.77782 2.96526 0 4.27251
1.6 −1.29986 0 −0.310353 −2.12386 0 −3.41757 3.00315 0 2.76073
1.7 −1.01172 0 −0.976420 4.44905 0 2.99336 3.01131 0 −4.50120
1.8 −0.521281 0 −1.72827 0.302159 0 0.215327 1.94347 0 −0.157510
1.9 −0.455991 0 −1.79207 −3.13439 0 0.856728 1.72915 0 1.42925
1.10 −0.0682043 0 −1.99535 1.18434 0 −4.66035 0.272500 0 −0.0807768
1.11 0.563863 0 −1.68206 4.27233 0 0.945321 −2.07618 0 2.40901
1.12 0.878744 0 −1.22781 1.62071 0 2.93534 −2.83642 0 1.42419
1.13 1.02284 0 −0.953805 2.76466 0 −3.04869 −3.02126 0 2.82779
1.14 1.38639 0 −0.0779333 −2.26790 0 −0.965210 −2.88082 0 −3.14419
1.15 1.40249 0 −0.0330274 −1.97794 0 1.49830 −2.85130 0 −2.77404
1.16 1.57842 0 0.491400 2.27349 0 2.42031 −2.38120 0 3.58851
1.17 1.73645 0 1.01527 −0.0241179 0 −4.08219 −1.70994 0 −0.0418795
1.18 2.38894 0 3.70703 −1.18459 0 −1.03676 4.07800 0 −2.82991
1.19 2.51933 0 4.34701 0.0919030 0 4.54767 5.91287 0 0.231534
1.20 2.64385 0 4.98995 1.69587 0 0.416922 7.90499 0 4.48364
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.f yes 21
3.b odd 2 1 8019.2.a.c ✓ 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8019.2.a.c ✓ 21 3.b odd 2 1
8019.2.a.f yes 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{21} - 6 T_{2}^{20} - 12 T_{2}^{19} + 130 T_{2}^{18} - 24 T_{2}^{17} - 1146 T_{2}^{16} + 1083 T_{2}^{15} + \cdots - 53 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\). Copy content Toggle raw display