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Properties

Label 8019.2.a.i
Level $8019$
Weight $2$
Character orbit 8019.a
Self dual yes
Analytic conductor $64.032$
Analytic rank $1$
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: \(1\)
Dimension: \(48\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, 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 −2.78677 0 5.76607 0.0591933 0 0.765141 −10.4952 0 −0.164958
1.2 −2.76227 0 5.63012 1.74188 0 4.23367 −10.0274 0 −4.81154
1.3 −2.74869 0 5.55528 −3.20604 0 −4.29093 −9.77234 0 8.81241
1.4 −2.58854 0 4.70056 −3.46451 0 0.848497 −6.99050 0 8.96803
1.5 −2.49176 0 4.20888 3.55698 0 −4.04430 −5.50400 0 −8.86315
1.6 −2.48985 0 4.19936 −1.09265 0 2.65687 −5.47609 0 2.72053
1.7 −2.27724 0 3.18582 −3.40276 0 0.928464 −2.70039 0 7.74890
1.8 −2.25095 0 3.06678 −2.01161 0 −1.18945 −2.40127 0 4.52804
1.9 −2.16515 0 2.68787 3.05787 0 3.25666 −1.48933 0 −6.62075
1.10 −2.04918 0 2.19916 −3.85227 0 4.47630 −0.408107 0 7.89402
1.11 −1.93884 0 1.75908 −0.334950 0 −4.22786 0.467097 0 0.649413
1.12 −1.81767 0 1.30394 3.09910 0 0.137252 1.26521 0 −5.63316
1.13 −1.69020 0 0.856762 −0.595209 0 0.410093 1.93230 0 1.00602
1.14 −1.56489 0 0.448896 −4.28242 0 1.60202 2.42731 0 6.70153
1.15 −1.53979 0 0.370949 1.28583 0 3.45759 2.50839 0 −1.97991
1.16 −1.42916 0 0.0424985 −0.596655 0 −4.06486 2.79758 0 0.852715
1.17 −1.23478 0 −0.475321 2.26882 0 −3.95112 3.05647 0 −2.80149
1.18 −1.04797 0 −0.901755 −2.67790 0 1.71332 3.04096 0 2.80637
1.19 −0.892531 0 −1.20339 −2.80076 0 −1.37622 2.85912 0 2.49977
1.20 −0.724143 0 −1.47562 2.15850 0 −0.509330 2.51684 0 −1.56306
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.i ✓ 48
3.b odd 2 1 8019.2.a.j yes 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8019.2.a.i ✓ 48 1.a even 1 1 trivial
8019.2.a.j yes 48 3.b odd 2 1

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