Properties

Label 5929.2.a.e
Level $5929$
Weight $2$
Character orbit 5929.a
Self dual yes
Analytic conductor $47.343$
Analytic rank $0$
Dimension $1$
CM discriminant -11
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5929,2,Mod(1,5929)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5929, 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("5929.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5929 = 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5929.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: \(47.3433033584\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 121)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{3} - 2 q^{4} + 3 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - 2 q^{4} + 3 q^{5} - 2 q^{9} - 2 q^{12} + 3 q^{15} + 4 q^{16} - 6 q^{20} - 9 q^{23} + 4 q^{25} - 5 q^{27} + 5 q^{31} + 4 q^{36} + 7 q^{37} - 6 q^{45} + 12 q^{47} + 4 q^{48} + 6 q^{53} + 15 q^{59} - 6 q^{60} - 8 q^{64} + 13 q^{67} - 9 q^{69} - 3 q^{71} + 4 q^{75} + 12 q^{80} + q^{81} + 9 q^{89} + 18 q^{92} + 5 q^{93} - 17 q^{97}+O(q^{100}) \) 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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 1.00000 −2.00000 3.00000 0 0 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(11\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 CM by \(\Q(\sqrt{-11}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5929.2.a.e 1
7.b odd 2 1 121.2.a.b 1
11.b odd 2 1 CM 5929.2.a.e 1
21.c even 2 1 1089.2.a.g 1
28.d even 2 1 1936.2.a.h 1
35.c odd 2 1 3025.2.a.d 1
56.e even 2 1 7744.2.a.n 1
56.h odd 2 1 7744.2.a.bb 1
77.b even 2 1 121.2.a.b 1
77.j odd 10 4 121.2.c.c 4
77.l even 10 4 121.2.c.c 4
231.h odd 2 1 1089.2.a.g 1
308.g odd 2 1 1936.2.a.h 1
385.h even 2 1 3025.2.a.d 1
616.g odd 2 1 7744.2.a.n 1
616.o even 2 1 7744.2.a.bb 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
121.2.a.b 1 7.b odd 2 1
121.2.a.b 1 77.b even 2 1
121.2.c.c 4 77.j odd 10 4
121.2.c.c 4 77.l even 10 4
1089.2.a.g 1 21.c even 2 1
1089.2.a.g 1 231.h odd 2 1
1936.2.a.h 1 28.d even 2 1
1936.2.a.h 1 308.g odd 2 1
3025.2.a.d 1 35.c odd 2 1
3025.2.a.d 1 385.h even 2 1
5929.2.a.e 1 1.a even 1 1 trivial
5929.2.a.e 1 11.b odd 2 1 CM
7744.2.a.n 1 56.e even 2 1
7744.2.a.n 1 616.g odd 2 1
7744.2.a.bb 1 56.h odd 2 1
7744.2.a.bb 1 616.o even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5929))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{5} - 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 9 \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T - 5 \) Copy content Toggle raw display
$37$ \( T - 7 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T - 12 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 15 \) Copy content Toggle raw display
$61$ \( T \) Copy content Toggle raw display
$67$ \( T - 13 \) Copy content Toggle raw display
$71$ \( T + 3 \) Copy content Toggle raw display
$73$ \( T \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 9 \) Copy content Toggle raw display
$97$ \( T + 17 \) Copy content Toggle raw display
show more
show less