Properties

Label 5184.2.a.q
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 18)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{7} + O(q^{10}) \) \( q + 2q^{7} - 3q^{11} - 2q^{13} + 3q^{17} + q^{19} + 6q^{23} - 5q^{25} + 6q^{29} - 4q^{31} + 4q^{37} - 9q^{41} + q^{43} + 6q^{47} - 3q^{49} + 12q^{53} + 3q^{59} - 8q^{61} - 5q^{67} + 12q^{71} + 11q^{73} - 6q^{77} - 4q^{79} + 12q^{83} - 6q^{89} - 4q^{91} + 5q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

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

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.q 1
3.b odd 2 1 5184.2.a.r 1
4.b odd 2 1 5184.2.a.p 1
8.b even 2 1 162.2.a.b 1
8.d odd 2 1 1296.2.a.f 1
9.c even 3 2 1728.2.i.e 2
9.d odd 6 2 576.2.i.g 2
12.b even 2 1 5184.2.a.o 1
24.f even 2 1 1296.2.a.g 1
24.h odd 2 1 162.2.a.c 1
36.f odd 6 2 1728.2.i.f 2
36.h even 6 2 576.2.i.a 2
40.f even 2 1 4050.2.a.v 1
40.i odd 4 2 4050.2.c.r 2
56.h odd 2 1 7938.2.a.i 1
72.j odd 6 2 18.2.c.a 2
72.l even 6 2 144.2.i.c 2
72.n even 6 2 54.2.c.a 2
72.p odd 6 2 432.2.i.b 2
120.i odd 2 1 4050.2.a.c 1
120.w even 4 2 4050.2.c.c 2
168.i even 2 1 7938.2.a.x 1
360.bh odd 6 2 450.2.e.i 2
360.bk even 6 2 1350.2.e.c 2
360.br even 12 4 450.2.j.e 4
360.bu odd 12 4 1350.2.j.a 4
504.w even 6 2 2646.2.h.h 2
504.y even 6 2 882.2.h.b 2
504.bi odd 6 2 882.2.e.i 2
504.bn odd 6 2 2646.2.f.g 2
504.bp odd 6 2 2646.2.e.c 2
504.ca even 6 2 882.2.e.g 2
504.cc even 6 2 882.2.f.d 2
504.cq even 6 2 2646.2.e.b 2
504.cw odd 6 2 2646.2.h.i 2
504.db odd 6 2 882.2.h.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
18.2.c.a 2 72.j odd 6 2
54.2.c.a 2 72.n even 6 2
144.2.i.c 2 72.l even 6 2
162.2.a.b 1 8.b even 2 1
162.2.a.c 1 24.h odd 2 1
432.2.i.b 2 72.p odd 6 2
450.2.e.i 2 360.bh odd 6 2
450.2.j.e 4 360.br even 12 4
576.2.i.a 2 36.h even 6 2
576.2.i.g 2 9.d odd 6 2
882.2.e.g 2 504.ca even 6 2
882.2.e.i 2 504.bi odd 6 2
882.2.f.d 2 504.cc even 6 2
882.2.h.b 2 504.y even 6 2
882.2.h.c 2 504.db odd 6 2
1296.2.a.f 1 8.d odd 2 1
1296.2.a.g 1 24.f even 2 1
1350.2.e.c 2 360.bk even 6 2
1350.2.j.a 4 360.bu odd 12 4
1728.2.i.e 2 9.c even 3 2
1728.2.i.f 2 36.f odd 6 2
2646.2.e.b 2 504.cq even 6 2
2646.2.e.c 2 504.bp odd 6 2
2646.2.f.g 2 504.bn odd 6 2
2646.2.h.h 2 504.w even 6 2
2646.2.h.i 2 504.cw odd 6 2
4050.2.a.c 1 120.i odd 2 1
4050.2.a.v 1 40.f even 2 1
4050.2.c.c 2 120.w even 4 2
4050.2.c.r 2 40.i odd 4 2
5184.2.a.o 1 12.b even 2 1
5184.2.a.p 1 4.b odd 2 1
5184.2.a.q 1 1.a even 1 1 trivial
5184.2.a.r 1 3.b odd 2 1
7938.2.a.i 1 56.h odd 2 1
7938.2.a.x 1 168.i even 2 1

Hecke kernels

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

\( T_{5} \)
\( T_{7} - 2 \)
\( T_{11} + 3 \)

Hecke characteristic polynomials

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