Properties

Label 5544.2.a.h
Level $5544$
Weight $2$
Character orbit 5544.a
Self dual yes
Analytic conductor $44.269$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5544.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.2690628806\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1848)
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 \( q - q^{5} - q^{7} + q^{11} + 3 q^{13} + 7 q^{19} - 6 q^{23} - 4 q^{25} + 9 q^{29} + q^{35} - 3 q^{37} - 8 q^{41} + 10 q^{43} - 3 q^{47} + q^{49} - 6 q^{53} - q^{55} - 7 q^{59} + 10 q^{61} - 3 q^{65} - 3 q^{67} + 8 q^{71} - 7 q^{73} - q^{77} + 8 q^{79} + 6 q^{89} - 3 q^{91} - 7 q^{95} - 10 q^{97}+O(q^{100}) \) 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
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(1\)
\(11\) \(-1\)

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 5544.2.a.h 1
3.b odd 2 1 1848.2.a.k 1
12.b even 2 1 3696.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1848.2.a.k 1 3.b odd 2 1
3696.2.a.l 1 12.b even 2 1
5544.2.a.h 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5544))\):

\( T_{5} + 1 \) Copy content Toggle raw display
\( T_{13} - 3 \) 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
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T - 3 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 7 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T - 9 \) Copy content Toggle raw display
$31$ \( T \) Copy content Toggle raw display
$37$ \( T + 3 \) Copy content Toggle raw display
$41$ \( T + 8 \) Copy content Toggle raw display
$43$ \( T - 10 \) Copy content Toggle raw display
$47$ \( T + 3 \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T + 7 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 3 \) Copy content Toggle raw display
$71$ \( T - 8 \) Copy content Toggle raw display
$73$ \( T + 7 \) Copy content Toggle raw display
$79$ \( T - 8 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 6 \) Copy content Toggle raw display
$97$ \( T + 10 \) Copy content Toggle raw display
show more
show less