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Properties

Label 8019.2.a.d
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 18 q^{4} - 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q + 18 q^{4} - 12 q^{5} - 15 q^{10} + 21 q^{11} - 3 q^{13} + 12 q^{16} - 12 q^{17} + 12 q^{19} - 33 q^{20} - 12 q^{23} + 15 q^{25} - 21 q^{26} - 24 q^{28} - 33 q^{29} - 42 q^{31} - 6 q^{34} + 18 q^{35} - 9 q^{37} + 3 q^{38} - 30 q^{40} - 48 q^{41} + 6 q^{43} + 18 q^{44} + 81 q^{46} - 12 q^{47} + 39 q^{49} - 45 q^{50} - 9 q^{52} - 36 q^{53} - 12 q^{55} - 27 q^{56} - 24 q^{58} - 48 q^{59} + 18 q^{61} - 27 q^{62} - 42 q^{64} - 48 q^{65} - 54 q^{67} - 30 q^{68} + 9 q^{70} - 24 q^{71} + 21 q^{73} - 36 q^{74} + 69 q^{76} - 15 q^{79} - 18 q^{80} - 21 q^{82} + 6 q^{83} - 6 q^{86} - 60 q^{89} - 45 q^{91} - 30 q^{92} + 6 q^{94} - 24 q^{95} + 15 q^{98}+O(q^{100}) \) 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 −2.60346 0 4.77798 −2.82283 0 0.130606 −7.23235 0 7.34910
1.2 −2.53079 0 4.40490 3.26192 0 0.0697383 −6.08631 0 −8.25523
1.3 −2.04887 0 2.19786 2.31259 0 −3.38221 −0.405389 0 −4.73820
1.4 −1.94669 0 1.78959 −3.52215 0 2.10255 0.409595 0 6.85652
1.5 −1.88221 0 1.54271 −4.14021 0 −4.86369 0.860716 0 7.79275
1.6 −1.80440 0 1.25586 1.40203 0 4.40338 1.34272 0 −2.52982
1.7 −1.16321 0 −0.646948 0.889251 0 −1.29111 3.07895 0 −1.03438
1.8 −0.582496 0 −1.66070 −0.274097 0 −0.972494 2.13234 0 0.159660
1.9 −0.324457 0 −1.89473 3.44350 0 0.404165 1.26367 0 −1.11727
1.10 −0.299293 0 −1.91042 −2.44697 0 4.60423 1.17036 0 0.732360
1.11 −0.119914 0 −1.98562 −0.735213 0 3.25386 0.477932 0 0.0881623
1.12 −0.0758084 0 −1.99425 0.791360 0 −2.84148 0.302798 0 −0.0599917
1.13 0.635737 0 −1.59584 −1.93321 0 −4.14964 −2.28601 0 −1.22901
1.14 1.11183 0 −0.763828 1.55330 0 3.33735 −3.07291 0 1.72701
1.15 1.12895 0 −0.725462 −3.53436 0 −1.54937 −3.07692 0 −3.99013
1.16 1.33692 0 −0.212636 1.58522 0 2.87487 −2.95812 0 2.11931
1.17 1.65229 0 0.730066 −0.213393 0 2.87969 −2.09830 0 −0.352587
1.18 2.24158 0 3.02470 −1.17206 0 −3.56737 2.29694 0 −2.62728
1.19 2.34270 0 3.48827 −2.96239 0 3.40852 3.48657 0 −6.94000
1.20 2.37001 0 3.61697 0.161497 0 −3.13556 3.83224 0 0.382749
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.d ✓ 21
3.b odd 2 1 8019.2.a.e yes 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8019.2.a.d ✓ 21 1.a even 1 1 trivial
8019.2.a.e yes 21 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{21} - 30 T_{2}^{19} + 378 T_{2}^{17} - 2601 T_{2}^{15} + 3 T_{2}^{14} + 10641 T_{2}^{13} + \cdots - 3 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\). Copy content Toggle raw display