↑

Properties

Label 7803.2.a.cg
Level $7803$
Weight $2$
Character orbit 7803.a
Self dual yes
Analytic conductor $62.307$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7803,2,Mod(1,7803)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7803, 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("7803.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7803 = 3^{3} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7803.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: \(62.3072686972\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 459)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} + 20 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} + 20 q^{5} + 8 q^{11} + 4 q^{13} + 16 q^{14} + 24 q^{16} + 4 q^{19} + 48 q^{20} + 36 q^{23} + 28 q^{25} + 64 q^{29} + 36 q^{41} + 4 q^{43} + 16 q^{44} + 24 q^{49} + 16 q^{52} + 20 q^{55} + 80 q^{56} - 16 q^{62} - 24 q^{64} + 72 q^{65} + 16 q^{67} - 48 q^{70} + 72 q^{71} + 80 q^{74} - 40 q^{76} + 104 q^{80} + 144 q^{92} - 72 q^{94} - 12 q^{95}+O(q^{100}) \) 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 −2.60090 0 4.76468 0.911981 0 −3.17536 −7.19066 0 −2.37197
1.2 −2.55639 0 4.53515 1.29372 0 −0.565179 −6.48083 0 −3.30726
1.3 −2.43845 0 3.94605 3.97925 0 −2.33633 −4.74536 0 −9.70321
1.4 −2.21855 0 2.92198 4.14266 0 3.37488 −2.04547 0 −9.19071
1.5 −2.02384 0 2.09592 −3.35608 0 −2.56592 −0.194125 0 6.79216
1.6 −1.55801 0 0.427381 −0.0815910 0 1.81716 2.45015 0 0.127119
1.7 −1.55047 0 0.403950 −1.95745 0 0.219625 2.47462 0 3.03496
1.8 −1.27156 0 −0.383141 1.88026 0 0.231288 3.03030 0 −2.39086
1.9 −0.944803 0 −1.10735 1.64416 0 4.63507 2.93583 0 −1.55341
1.10 −0.533361 0 −1.71553 −2.01564 0 −2.52795 1.98172 0 1.07506
1.11 −0.313123 0 −1.90195 −0.0595634 0 −2.67689 1.22179 0 0.0186507
1.12 −0.113371 0 −1.98715 3.61829 0 −4.87047 0.452028 0 −0.410211
1.13 0.113371 0 −1.98715 3.61829 0 4.87047 −0.452028 0 0.410211
1.14 0.313123 0 −1.90195 −0.0595634 0 2.67689 −1.22179 0 −0.0186507
1.15 0.533361 0 −1.71553 −2.01564 0 2.52795 −1.98172 0 −1.07506
1.16 0.944803 0 −1.10735 1.64416 0 −4.63507 −2.93583 0 1.55341
1.17 1.27156 0 −0.383141 1.88026 0 −0.231288 −3.03030 0 2.39086
1.18 1.55047 0 0.403950 −1.95745 0 −0.219625 −2.47462 0 −3.03496
1.19 1.55801 0 0.427381 −0.0815910 0 −1.81716 −2.45015 0 −0.127119
1.20 2.02384 0 2.09592 −3.35608 0 2.56592 0.194125 0 −6.79216
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(17\) \(-1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
51.c odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7803.2.a.cg 24
3.b odd 2 1 7803.2.a.cd 24
17.b even 2 1 7803.2.a.cd 24
17.e odd 16 2 459.2.l.a ✓ 48
51.c odd 2 1 inner 7803.2.a.cg 24
51.i even 16 2 459.2.l.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
459.2.l.a ✓ 48 17.e odd 16 2
459.2.l.a ✓ 48 51.i even 16 2
7803.2.a.cd 24 3.b odd 2 1
7803.2.a.cd 24 17.b even 2 1
7803.2.a.cg 24 1.a even 1 1 trivial
7803.2.a.cg 24 51.c odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7803))\):

\( T_{2}^{24} - 36 T_{2}^{22} + 558 T_{2}^{20} - 4876 T_{2}^{18} + 26426 T_{2}^{16} - 92104 T_{2}^{14} + \cdots + 16 \) Copy content Toggle raw display
\( T_{5}^{12} - 10 T_{5}^{11} + 13 T_{5}^{10} + 156 T_{5}^{9} - 500 T_{5}^{8} - 360 T_{5}^{7} + 2964 T_{5}^{6} + \cdots - 14 \) Copy content Toggle raw display
\( T_{7}^{24} - 96 T_{7}^{22} + 3892 T_{7}^{20} - 87680 T_{7}^{18} + 1215096 T_{7}^{16} - 10798488 T_{7}^{14} + \cdots + 262144 \) Copy content Toggle raw display
\( T_{11}^{12} - 4 T_{11}^{11} - 64 T_{11}^{10} + 320 T_{11}^{9} + 957 T_{11}^{8} - 7068 T_{11}^{7} + \cdots + 6172 \) Copy content Toggle raw display