Properties

Label 1080.2.a.e
Level $1080$
Weight $2$
Character orbit 1080.a
Self dual yes
Analytic conductor $8.624$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.62384341830\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} + 2q^{7} + O(q^{10}) \) \( q - q^{5} + 2q^{7} - 4q^{11} - 2q^{13} - 5q^{17} - 5q^{19} - q^{23} + q^{25} + 2q^{29} + 7q^{31} - 2q^{35} - 6q^{37} + 4q^{43} - 4q^{47} - 3q^{49} - 9q^{53} + 4q^{55} - 14q^{59} - 11q^{61} + 2q^{65} + 14q^{67} - 12q^{73} - 8q^{77} - 3q^{79} + q^{83} + 5q^{85} - 4q^{91} + 5q^{95} + 16q^{97} + O(q^{100}) \)

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 −1.00000 0 2.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)

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 1080.2.a.e 1
3.b odd 2 1 1080.2.a.l yes 1
4.b odd 2 1 2160.2.a.e 1
5.b even 2 1 5400.2.a.j 1
5.c odd 4 2 5400.2.f.f 2
8.b even 2 1 8640.2.a.cd 1
8.d odd 2 1 8640.2.a.bi 1
9.c even 3 2 3240.2.q.p 2
9.d odd 6 2 3240.2.q.b 2
12.b even 2 1 2160.2.a.m 1
15.d odd 2 1 5400.2.a.q 1
15.e even 4 2 5400.2.f.x 2
24.f even 2 1 8640.2.a.k 1
24.h odd 2 1 8640.2.a.t 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1080.2.a.e 1 1.a even 1 1 trivial
1080.2.a.l yes 1 3.b odd 2 1
2160.2.a.e 1 4.b odd 2 1
2160.2.a.m 1 12.b even 2 1
3240.2.q.b 2 9.d odd 6 2
3240.2.q.p 2 9.c even 3 2
5400.2.a.j 1 5.b even 2 1
5400.2.a.q 1 15.d odd 2 1
5400.2.f.f 2 5.c odd 4 2
5400.2.f.x 2 15.e even 4 2
8640.2.a.k 1 24.f even 2 1
8640.2.a.t 1 24.h odd 2 1
8640.2.a.bi 1 8.d odd 2 1
8640.2.a.cd 1 8.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\):

\( T_{7} - 2 \)
\( T_{11} + 4 \)
\( T_{17} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( -2 + T \)
$11$ \( 4 + T \)
$13$ \( 2 + T \)
$17$ \( 5 + T \)
$19$ \( 5 + T \)
$23$ \( 1 + T \)
$29$ \( -2 + T \)
$31$ \( -7 + T \)
$37$ \( 6 + T \)
$41$ \( T \)
$43$ \( -4 + T \)
$47$ \( 4 + T \)
$53$ \( 9 + T \)
$59$ \( 14 + T \)
$61$ \( 11 + T \)
$67$ \( -14 + T \)
$71$ \( T \)
$73$ \( 12 + T \)
$79$ \( 3 + T \)
$83$ \( -1 + T \)
$89$ \( T \)
$97$ \( -16 + T \)
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