Properties

Label 5472.2.a.q
Level $5472$
Weight $2$
Character orbit 5472.a
Self dual yes
Analytic conductor $43.694$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.6941399860\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 608)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5} + q^{7} + O(q^{10}) \) \( q + q^{5} + q^{7} + 3 q^{11} - 4 q^{13} + 3 q^{17} - q^{19} - 8 q^{23} - 4 q^{25} - 2 q^{31} + q^{35} - 8 q^{37} - 11 q^{43} - 7 q^{47} - 6 q^{49} - 2 q^{53} + 3 q^{55} + 6 q^{59} - q^{61} - 4 q^{65} + 10 q^{67} + 2 q^{71} + 5 q^{73} + 3 q^{77} + 2 q^{79} + 3 q^{85} - 6 q^{89} - 4 q^{91} - q^{95} - 12 q^{97} + O(q^{100}) \)

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
\(2\) \(-1\)
\(3\) \(-1\)
\(19\) \(1\)

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 5472.2.a.q 1
3.b odd 2 1 608.2.a.c yes 1
4.b odd 2 1 5472.2.a.m 1
12.b even 2 1 608.2.a.b 1
24.f even 2 1 1216.2.a.j 1
24.h odd 2 1 1216.2.a.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
608.2.a.b 1 12.b even 2 1
608.2.a.c yes 1 3.b odd 2 1
1216.2.a.j 1 24.f even 2 1
1216.2.a.k 1 24.h odd 2 1
5472.2.a.m 1 4.b odd 2 1
5472.2.a.q 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5472))\):

\( T_{5} - 1 \)
\( T_{7} - 1 \)
\( T_{11} - 3 \)
\( T_{13} + 4 \)
\( T_{23} + 8 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( -3 + T \)
$13$ \( 4 + T \)
$17$ \( -3 + T \)
$19$ \( 1 + T \)
$23$ \( 8 + T \)
$29$ \( T \)
$31$ \( 2 + T \)
$37$ \( 8 + T \)
$41$ \( T \)
$43$ \( 11 + T \)
$47$ \( 7 + T \)
$53$ \( 2 + T \)
$59$ \( -6 + T \)
$61$ \( 1 + T \)
$67$ \( -10 + T \)
$71$ \( -2 + T \)
$73$ \( -5 + T \)
$79$ \( -2 + T \)
$83$ \( T \)
$89$ \( 6 + T \)
$97$ \( 12 + T \)
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