Properties

Label 6480.2.a.q
Level $6480$
Weight $2$
Character orbit 6480.a
Self dual yes
Analytic conductor $51.743$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6480.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.7430605098\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 360)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5} + O(q^{10}) \) \( q + q^{5} - 5q^{11} - 3q^{17} - 5q^{19} + 6q^{23} + q^{25} + 10q^{29} + 2q^{31} + 4q^{37} + 3q^{41} - 3q^{43} + 4q^{47} - 7q^{49} + 6q^{53} - 5q^{55} - 3q^{59} + 2q^{61} + 11q^{67} - 14q^{71} - 15q^{73} - 10q^{79} - 12q^{83} - 3q^{85} - 14q^{89} - 5q^{95} - 13q^{97} + O(q^{100}) \)

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 0 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 6480.2.a.q 1
3.b odd 2 1 6480.2.a.e 1
4.b odd 2 1 3240.2.a.f 1
9.c even 3 2 2160.2.q.c 2
9.d odd 6 2 720.2.q.e 2
12.b even 2 1 3240.2.a.b 1
36.f odd 6 2 1080.2.q.a 2
36.h even 6 2 360.2.q.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
360.2.q.a 2 36.h even 6 2
720.2.q.e 2 9.d odd 6 2
1080.2.q.a 2 36.f odd 6 2
2160.2.q.c 2 9.c even 3 2
3240.2.a.b 1 12.b even 2 1
3240.2.a.f 1 4.b odd 2 1
6480.2.a.e 1 3.b odd 2 1
6480.2.a.q 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6480))\):

\( T_{7} \)
\( T_{11} + 5 \)
\( T_{13} \)
\( T_{17} + 3 \)
\( T_{19} + 5 \)
\( T_{23} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( T \)
$11$ \( 5 + T \)
$13$ \( T \)
$17$ \( 3 + T \)
$19$ \( 5 + T \)
$23$ \( -6 + T \)
$29$ \( -10 + T \)
$31$ \( -2 + T \)
$37$ \( -4 + T \)
$41$ \( -3 + T \)
$43$ \( 3 + T \)
$47$ \( -4 + T \)
$53$ \( -6 + T \)
$59$ \( 3 + T \)
$61$ \( -2 + T \)
$67$ \( -11 + T \)
$71$ \( 14 + T \)
$73$ \( 15 + T \)
$79$ \( 10 + T \)
$83$ \( 12 + T \)
$89$ \( 14 + T \)
$97$ \( 13 + T \)
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