Properties

Label 5808.2.a.bh
Level $5808$
Weight $2$
Character orbit 5808.a
Self dual yes
Analytic conductor $46.377$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5808,2,Mod(1,5808)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5808, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("5808.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5808 = 2^{4} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5808.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: \(46.3771134940\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 363)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{3} + 4 q^{5} - q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} + 4 q^{5} - q^{7} + q^{9} - 2 q^{13} + 4 q^{15} + 4 q^{17} + 3 q^{19} - q^{21} - 2 q^{23} + 11 q^{25} + q^{27} + 6 q^{29} + 5 q^{31} - 4 q^{35} + 3 q^{37} - 2 q^{39} - 2 q^{41} - 12 q^{43} + 4 q^{45} - 2 q^{47} - 6 q^{49} + 4 q^{51} + 6 q^{53} + 3 q^{57} + 10 q^{59} + 3 q^{61} - q^{63} - 8 q^{65} + q^{67} - 2 q^{69} - 11 q^{73} + 11 q^{75} - 11 q^{79} + q^{81} - 6 q^{83} + 16 q^{85} + 6 q^{87} + 12 q^{89} + 2 q^{91} + 5 q^{93} + 12 q^{95} + 5 q^{97}+O(q^{100}) \) 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 0 4.00000 0 −1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(11\) \(-1\)

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 5808.2.a.bh 1
4.b odd 2 1 363.2.a.a 1
11.b odd 2 1 5808.2.a.bi 1
12.b even 2 1 1089.2.a.k 1
20.d odd 2 1 9075.2.a.t 1
44.c even 2 1 363.2.a.c yes 1
44.g even 10 4 363.2.e.d 4
44.h odd 10 4 363.2.e.i 4
132.d odd 2 1 1089.2.a.a 1
220.g even 2 1 9075.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
363.2.a.a 1 4.b odd 2 1
363.2.a.c yes 1 44.c even 2 1
363.2.e.d 4 44.g even 10 4
363.2.e.i 4 44.h odd 10 4
1089.2.a.a 1 132.d odd 2 1
1089.2.a.k 1 12.b even 2 1
5808.2.a.bh 1 1.a even 1 1 trivial
5808.2.a.bi 1 11.b odd 2 1
9075.2.a.b 1 220.g even 2 1
9075.2.a.t 1 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5808))\):

\( T_{5} - 4 \) Copy content Toggle raw display
\( T_{7} + 1 \) Copy content Toggle raw display
\( T_{13} + 2 \) 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
$5$ \( T - 4 \) Copy content Toggle raw display
$7$ \( T + 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T + 2 \) Copy content Toggle raw display
$17$ \( T - 4 \) Copy content Toggle raw display
$19$ \( T - 3 \) Copy content Toggle raw display
$23$ \( T + 2 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T - 5 \) Copy content Toggle raw display
$37$ \( T - 3 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T + 12 \) Copy content Toggle raw display
$47$ \( T + 2 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 10 \) Copy content Toggle raw display
$61$ \( T - 3 \) Copy content Toggle raw display
$67$ \( T - 1 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T + 11 \) Copy content Toggle raw display
$79$ \( T + 11 \) Copy content Toggle raw display
$83$ \( T + 6 \) Copy content Toggle raw display
$89$ \( T - 12 \) Copy content Toggle raw display
$97$ \( T - 5 \) Copy content Toggle raw display
show more
show less