Properties

Label 1584.2.a.n
Level $1584$
Weight $2$
Character orbit 1584.a
Self dual yes
Analytic conductor $12.648$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.6483036802\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 264)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{5} - 4q^{7} + O(q^{10}) \) \( q + 2q^{5} - 4q^{7} - q^{11} + 6q^{13} - 6q^{17} + 8q^{19} - q^{25} + 6q^{29} - 8q^{35} + 6q^{37} + 10q^{41} + 8q^{43} + 9q^{49} - 6q^{53} - 2q^{55} + 4q^{59} - 2q^{61} + 12q^{65} + 12q^{67} - 8q^{71} + 2q^{73} + 4q^{77} + 4q^{79} - 12q^{83} - 12q^{85} + 6q^{89} - 24q^{91} + 16q^{95} + 2q^{97} + O(q^{100}) \)

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 2.00000 0 −4.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(11\) \(1\)

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 1584.2.a.n 1
3.b odd 2 1 528.2.a.b 1
4.b odd 2 1 792.2.a.f 1
8.b even 2 1 6336.2.a.o 1
8.d odd 2 1 6336.2.a.v 1
12.b even 2 1 264.2.a.b 1
24.f even 2 1 2112.2.a.m 1
24.h odd 2 1 2112.2.a.y 1
33.d even 2 1 5808.2.a.f 1
44.c even 2 1 8712.2.a.r 1
60.h even 2 1 6600.2.a.a 1
60.l odd 4 2 6600.2.d.n 2
132.d odd 2 1 2904.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
264.2.a.b 1 12.b even 2 1
528.2.a.b 1 3.b odd 2 1
792.2.a.f 1 4.b odd 2 1
1584.2.a.n 1 1.a even 1 1 trivial
2112.2.a.m 1 24.f even 2 1
2112.2.a.y 1 24.h odd 2 1
2904.2.a.i 1 132.d odd 2 1
5808.2.a.f 1 33.d even 2 1
6336.2.a.o 1 8.b even 2 1
6336.2.a.v 1 8.d odd 2 1
6600.2.a.a 1 60.h even 2 1
6600.2.d.n 2 60.l odd 4 2
8712.2.a.r 1 44.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\):

\( T_{5} - 2 \)
\( T_{7} + 4 \)
\( T_{13} - 6 \)
\( T_{17} + 6 \)