Properties

Label 2592.2.a.h
Level $2592$
Weight $2$
Character orbit 2592.a
Self dual yes
Analytic conductor $20.697$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 288)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 4 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 4 q^{5} + 2 q^{7} + 5 q^{11} - 2 q^{13} - 3 q^{17} - q^{19} + 6 q^{23} + 11 q^{25} - 2 q^{29} + 4 q^{31} + 8 q^{35} - 8 q^{37} + q^{41} + 7 q^{43} - 2 q^{47} - 3 q^{49} - 4 q^{53} + 20 q^{55} - 5 q^{59} - 8 q^{65} + 13 q^{67} - 8 q^{71} + 3 q^{73} + 10 q^{77} - 8 q^{79} - 12 q^{83} - 12 q^{85} - 10 q^{89} - 4 q^{91} - 4 q^{95} - 11 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

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 2592.2.a.h 1
3.b odd 2 1 2592.2.a.b 1
4.b odd 2 1 2592.2.a.g 1
8.b even 2 1 5184.2.a.b 1
8.d odd 2 1 5184.2.a.a 1
9.c even 3 2 288.2.i.a 2
9.d odd 6 2 864.2.i.a 2
12.b even 2 1 2592.2.a.a 1
24.f even 2 1 5184.2.a.be 1
24.h odd 2 1 5184.2.a.bf 1
36.f odd 6 2 288.2.i.b yes 2
36.h even 6 2 864.2.i.b 2
72.j odd 6 2 1728.2.i.a 2
72.l even 6 2 1728.2.i.b 2
72.n even 6 2 576.2.i.h 2
72.p odd 6 2 576.2.i.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
288.2.i.a 2 9.c even 3 2
288.2.i.b yes 2 36.f odd 6 2
576.2.i.b 2 72.p odd 6 2
576.2.i.h 2 72.n even 6 2
864.2.i.a 2 9.d odd 6 2
864.2.i.b 2 36.h even 6 2
1728.2.i.a 2 72.j odd 6 2
1728.2.i.b 2 72.l even 6 2
2592.2.a.a 1 12.b even 2 1
2592.2.a.b 1 3.b odd 2 1
2592.2.a.g 1 4.b odd 2 1
2592.2.a.h 1 1.a even 1 1 trivial
5184.2.a.a 1 8.d odd 2 1
5184.2.a.b 1 8.b even 2 1
5184.2.a.be 1 24.f even 2 1
5184.2.a.bf 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2592))\):

\( T_{5} - 4 \) Copy content Toggle raw display
\( T_{7} - 2 \) Copy content Toggle raw display
\( T_{11} - 5 \) Copy content Toggle raw display

Hecke characteristic polynomials

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