Properties

Label 2160.2.a.s
Level $2160$
Weight $2$
Character orbit 2160.a
Self dual yes
Analytic conductor $17.248$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.2476868366\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 540)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{5} + q^{7} - 6 q^{11} - q^{13} + q^{19} - 6 q^{23} + q^{25} + 6 q^{29} - 8 q^{31} + q^{35} - 7 q^{37} - 6 q^{41} + 4 q^{43} - 12 q^{47} - 6 q^{49} - 6 q^{53} - 6 q^{55} + 11 q^{61} - q^{65} + 7 q^{67} + 6 q^{71} + 11 q^{73} - 6 q^{77} + q^{79} - 6 q^{83} - 12 q^{89} - q^{91} + q^{95} - 13 q^{97}+O(q^{100}) \) 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.

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 0 0 1.00000 0 1.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(-1\)

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 2160.2.a.s 1
3.b odd 2 1 2160.2.a.h 1
4.b odd 2 1 540.2.a.e yes 1
8.b even 2 1 8640.2.a.s 1
8.d odd 2 1 8640.2.a.l 1
12.b even 2 1 540.2.a.b 1
20.d odd 2 1 2700.2.a.m 1
20.e even 4 2 2700.2.d.k 2
24.f even 2 1 8640.2.a.br 1
24.h odd 2 1 8640.2.a.bu 1
36.f odd 6 2 1620.2.i.d 2
36.h even 6 2 1620.2.i.j 2
60.h even 2 1 2700.2.a.k 1
60.l odd 4 2 2700.2.d.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
540.2.a.b 1 12.b even 2 1
540.2.a.e yes 1 4.b odd 2 1
1620.2.i.d 2 36.f odd 6 2
1620.2.i.j 2 36.h even 6 2
2160.2.a.h 1 3.b odd 2 1
2160.2.a.s 1 1.a even 1 1 trivial
2700.2.a.k 1 60.h even 2 1
2700.2.a.m 1 20.d odd 2 1
2700.2.d.a 2 60.l odd 4 2
2700.2.d.k 2 20.e even 4 2
8640.2.a.l 1 8.d odd 2 1
8640.2.a.s 1 8.b even 2 1
8640.2.a.br 1 24.f even 2 1
8640.2.a.bu 1 24.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2160))\):

\( T_{7} - 1 \) Copy content Toggle raw display
\( T_{11} + 6 \) Copy content Toggle raw display
\( T_{13} + 1 \) Copy content Toggle raw display
\( T_{17} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T + 6 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 1 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T + 8 \) Copy content Toggle raw display
$37$ \( T + 7 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T + 12 \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 11 \) Copy content Toggle raw display
$67$ \( T - 7 \) Copy content Toggle raw display
$71$ \( T - 6 \) Copy content Toggle raw display
$73$ \( T - 11 \) Copy content Toggle raw display
$79$ \( T - 1 \) Copy content Toggle raw display
$83$ \( T + 6 \) Copy content Toggle raw display
$89$ \( T + 12 \) Copy content Toggle raw display
$97$ \( T + 13 \) Copy content Toggle raw display
show more
show less