Properties

Label 1584.2.a.r
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 99)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 4 q^{5} + 2 q^{7} + O(q^{10}) \) \( q + 4 q^{5} + 2 q^{7} - q^{11} - 2 q^{13} - 2 q^{17} + 6 q^{19} + 4 q^{23} + 11 q^{25} + 6 q^{29} - 4 q^{31} + 8 q^{35} - 6 q^{37} + 10 q^{41} - 6 q^{43} - 8 q^{47} - 3 q^{49} - 4 q^{55} + 4 q^{59} - 6 q^{61} - 8 q^{65} - 8 q^{67} - 2 q^{73} - 2 q^{77} + 10 q^{79} + 12 q^{83} - 8 q^{85} - 4 q^{91} + 24 q^{95} + 2 q^{97} + O(q^{100}) \)

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 4.00000 0 2.00000 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.r 1
3.b odd 2 1 1584.2.a.b 1
4.b odd 2 1 99.2.a.c yes 1
8.b even 2 1 6336.2.a.f 1
8.d odd 2 1 6336.2.a.b 1
12.b even 2 1 99.2.a.a 1
20.d odd 2 1 2475.2.a.c 1
20.e even 4 2 2475.2.c.g 2
24.f even 2 1 6336.2.a.cl 1
24.h odd 2 1 6336.2.a.cm 1
28.d even 2 1 4851.2.a.o 1
36.f odd 6 2 891.2.e.c 2
36.h even 6 2 891.2.e.j 2
44.c even 2 1 1089.2.a.d 1
60.h even 2 1 2475.2.a.j 1
60.l odd 4 2 2475.2.c.b 2
84.h odd 2 1 4851.2.a.g 1
132.d odd 2 1 1089.2.a.h 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
99.2.a.a 1 12.b even 2 1
99.2.a.c yes 1 4.b odd 2 1
891.2.e.c 2 36.f odd 6 2
891.2.e.j 2 36.h even 6 2
1089.2.a.d 1 44.c even 2 1
1089.2.a.h 1 132.d odd 2 1
1584.2.a.b 1 3.b odd 2 1
1584.2.a.r 1 1.a even 1 1 trivial
2475.2.a.c 1 20.d odd 2 1
2475.2.a.j 1 60.h even 2 1
2475.2.c.b 2 60.l odd 4 2
2475.2.c.g 2 20.e even 4 2
4851.2.a.g 1 84.h odd 2 1
4851.2.a.o 1 28.d even 2 1
6336.2.a.b 1 8.d odd 2 1
6336.2.a.f 1 8.b even 2 1
6336.2.a.cl 1 24.f even 2 1
6336.2.a.cm 1 24.h odd 2 1

Hecke kernels

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

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

Hecke characteristic polynomials

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