Properties

Label 5184.2.a.bd
Level $5184$
Weight $2$
Character orbit 5184.a
Self dual yes
Analytic conductor $41.394$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 162)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3 q^{5} + 4 q^{7} + O(q^{10}) \) \( q + 3 q^{5} + 4 q^{7} + q^{13} - 3 q^{17} - 4 q^{19} + 4 q^{25} - 9 q^{29} + 4 q^{31} + 12 q^{35} + q^{37} + 6 q^{41} + 8 q^{43} + 12 q^{47} + 9 q^{49} + 6 q^{53} + q^{61} + 3 q^{65} - 4 q^{67} + 12 q^{71} + 11 q^{73} + 16 q^{79} - 12 q^{83} - 9 q^{85} - 3 q^{89} + 4 q^{91} - 12 q^{95} + 2 q^{97} + O(q^{100}) \)

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 3.00000 0 4.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 5184.2.a.bd 1
3.b odd 2 1 5184.2.a.h 1
4.b odd 2 1 5184.2.a.y 1
8.b even 2 1 1296.2.a.c 1
8.d odd 2 1 162.2.a.a 1
12.b even 2 1 5184.2.a.c 1
24.f even 2 1 162.2.a.d yes 1
24.h odd 2 1 1296.2.a.l 1
40.e odd 2 1 4050.2.a.bh 1
40.k even 4 2 4050.2.c.g 2
56.e even 2 1 7938.2.a.n 1
72.j odd 6 2 1296.2.i.b 2
72.l even 6 2 162.2.c.a 2
72.n even 6 2 1296.2.i.n 2
72.p odd 6 2 162.2.c.d 2
120.m even 2 1 4050.2.a.r 1
120.q odd 4 2 4050.2.c.n 2
168.e odd 2 1 7938.2.a.s 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
162.2.a.a 1 8.d odd 2 1
162.2.a.d yes 1 24.f even 2 1
162.2.c.a 2 72.l even 6 2
162.2.c.d 2 72.p odd 6 2
1296.2.a.c 1 8.b even 2 1
1296.2.a.l 1 24.h odd 2 1
1296.2.i.b 2 72.j odd 6 2
1296.2.i.n 2 72.n even 6 2
4050.2.a.r 1 120.m even 2 1
4050.2.a.bh 1 40.e odd 2 1
4050.2.c.g 2 40.k even 4 2
4050.2.c.n 2 120.q odd 4 2
5184.2.a.c 1 12.b even 2 1
5184.2.a.h 1 3.b odd 2 1
5184.2.a.y 1 4.b odd 2 1
5184.2.a.bd 1 1.a even 1 1 trivial
7938.2.a.n 1 56.e even 2 1
7938.2.a.s 1 168.e odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5184))\):

\( T_{5} - 3 \)
\( T_{7} - 4 \)
\( T_{11} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -3 + T \)
$7$ \( -4 + T \)
$11$ \( T \)
$13$ \( -1 + T \)
$17$ \( 3 + T \)
$19$ \( 4 + T \)
$23$ \( T \)
$29$ \( 9 + T \)
$31$ \( -4 + T \)
$37$ \( -1 + T \)
$41$ \( -6 + T \)
$43$ \( -8 + T \)
$47$ \( -12 + T \)
$53$ \( -6 + T \)
$59$ \( T \)
$61$ \( -1 + T \)
$67$ \( 4 + T \)
$71$ \( -12 + T \)
$73$ \( -11 + T \)
$79$ \( -16 + T \)
$83$ \( 12 + T \)
$89$ \( 3 + T \)
$97$ \( -2 + T \)
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