Properties

Label 4560.2.a.r
Level $4560$
Weight $2$
Character orbit 4560.a
Self dual yes
Analytic conductor $36.412$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.4117833217\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - q^{5} - 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - q^{5} - 2 q^{7} + q^{9} + 6 q^{11} - q^{15} + 2 q^{17} + q^{19} - 2 q^{21} - 4 q^{23} + q^{25} + q^{27} - 8 q^{29} + 8 q^{31} + 6 q^{33} + 2 q^{35} - 4 q^{37} - 4 q^{41} + 6 q^{43} - q^{45} + 12 q^{47} - 3 q^{49} + 2 q^{51} + 6 q^{53} - 6 q^{55} + q^{57} + 4 q^{59} + 2 q^{61} - 2 q^{63} + 8 q^{67} - 4 q^{69} + 6 q^{73} + q^{75} - 12 q^{77} - 8 q^{79} + q^{81} - 4 q^{83} - 2 q^{85} - 8 q^{87} - 4 q^{89} + 8 q^{93} - q^{95} + 12 q^{97} + 6 q^{99}+O(q^{100}) \) 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 1.00000 0 −1.00000 0 −2.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(19\) \(-1\)

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 4560.2.a.r 1
4.b odd 2 1 570.2.a.b 1
12.b even 2 1 1710.2.a.s 1
20.d odd 2 1 2850.2.a.y 1
20.e even 4 2 2850.2.d.j 2
60.h even 2 1 8550.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
570.2.a.b 1 4.b odd 2 1
1710.2.a.s 1 12.b even 2 1
2850.2.a.y 1 20.d odd 2 1
2850.2.d.j 2 20.e even 4 2
4560.2.a.r 1 1.a even 1 1 trivial
8550.2.a.g 1 60.h even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4560))\):

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