Properties

Label 5733.2.a.l
Level $5733$
Weight $2$
Character orbit 5733.a
Self dual yes
Analytic conductor $45.778$
Analytic rank $0$
Dimension $1$
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] = [5733,2,Mod(1,5733)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5733.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.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: \(45.7782354788\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
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)
 
\(f(q)\) \(=\) \( q + 2 q^{2} + 2 q^{4} - 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} + 2 q^{4} - 3 q^{5} - 6 q^{10} + 6 q^{11} + q^{13} - 4 q^{16} + 4 q^{17} - 5 q^{19} - 6 q^{20} + 12 q^{22} - 3 q^{23} + 4 q^{25} + 2 q^{26} + 5 q^{29} + 3 q^{31} - 8 q^{32} + 8 q^{34} - 4 q^{37} - 10 q^{38} - 6 q^{41} - q^{43} + 12 q^{44} - 6 q^{46} + 7 q^{47} + 8 q^{50} + 2 q^{52} + 9 q^{53} - 18 q^{55} + 10 q^{58} + 8 q^{59} + 10 q^{61} + 6 q^{62} - 8 q^{64} - 3 q^{65} - 6 q^{67} + 8 q^{68} + 8 q^{71} + 13 q^{73} - 8 q^{74} - 10 q^{76} + 3 q^{79} + 12 q^{80} - 12 q^{82} + 15 q^{83} - 12 q^{85} - 2 q^{86} + 3 q^{89} - 6 q^{92} + 14 q^{94} + 15 q^{95} - 7 q^{97}+O(q^{100}) \) 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
2.00000 0 2.00000 −3.00000 0 0 0 0 −6.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(13\) \(-1\)

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 5733.2.a.l 1
3.b odd 2 1 637.2.a.a 1
7.b odd 2 1 819.2.a.f 1
21.c even 2 1 91.2.a.a 1
21.g even 6 2 637.2.e.e 2
21.h odd 6 2 637.2.e.d 2
39.d odd 2 1 8281.2.a.l 1
84.h odd 2 1 1456.2.a.g 1
105.g even 2 1 2275.2.a.h 1
168.e odd 2 1 5824.2.a.t 1
168.i even 2 1 5824.2.a.s 1
273.g even 2 1 1183.2.a.b 1
273.o odd 4 2 1183.2.c.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.a.a 1 21.c even 2 1
637.2.a.a 1 3.b odd 2 1
637.2.e.d 2 21.h odd 6 2
637.2.e.e 2 21.g even 6 2
819.2.a.f 1 7.b odd 2 1
1183.2.a.b 1 273.g even 2 1
1183.2.c.b 2 273.o odd 4 2
1456.2.a.g 1 84.h odd 2 1
2275.2.a.h 1 105.g even 2 1
5733.2.a.l 1 1.a even 1 1 trivial
5824.2.a.s 1 168.i even 2 1
5824.2.a.t 1 168.e odd 2 1
8281.2.a.l 1 39.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5733))\):

\( T_{2} - 2 \) Copy content Toggle raw display
\( T_{5} + 3 \) Copy content Toggle raw display
\( T_{11} - 6 \) Copy content Toggle raw display
\( T_{17} - 4 \) Copy content Toggle raw display
\( T_{19} + 5 \) Copy content Toggle raw display
\( T_{31} - 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T + 3 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 6 \) Copy content Toggle raw display
$13$ \( T - 1 \) Copy content Toggle raw display
$17$ \( T - 4 \) Copy content Toggle raw display
$19$ \( T + 5 \) Copy content Toggle raw display
$23$ \( T + 3 \) Copy content Toggle raw display
$29$ \( T - 5 \) Copy content Toggle raw display
$31$ \( T - 3 \) Copy content Toggle raw display
$37$ \( T + 4 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T + 1 \) Copy content Toggle raw display
$47$ \( T - 7 \) Copy content Toggle raw display
$53$ \( T - 9 \) Copy content Toggle raw display
$59$ \( T - 8 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 6 \) Copy content Toggle raw display
$71$ \( T - 8 \) Copy content Toggle raw display
$73$ \( T - 13 \) Copy content Toggle raw display
$79$ \( T - 3 \) Copy content Toggle raw display
$83$ \( T - 15 \) Copy content Toggle raw display
$89$ \( T - 3 \) Copy content Toggle raw display
$97$ \( T + 7 \) Copy content Toggle raw display
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