Properties

Label 5040.2.a.bp
Level $5040$
Weight $2$
Character orbit 5040.a
Self dual yes
Analytic conductor $40.245$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5040.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.2446026187\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5} + q^{7} + O(q^{10}) \) \( q + q^{5} + q^{7} + 4q^{11} + 6q^{13} + 4q^{17} - 6q^{19} + q^{25} - 6q^{29} + 4q^{31} + q^{35} + 8q^{37} + 10q^{41} + 2q^{43} - 10q^{47} + q^{49} + 14q^{53} + 4q^{55} + 4q^{59} - 8q^{61} + 6q^{65} - 6q^{67} + 2q^{71} - 10q^{73} + 4q^{77} - 16q^{79} + 8q^{83} + 4q^{85} + 2q^{89} + 6q^{91} - 6q^{95} + 2q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(-1\)
\(7\) \(-1\)

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 5040.2.a.bp 1
3.b odd 2 1 5040.2.a.n 1
4.b odd 2 1 630.2.a.e 1
12.b even 2 1 630.2.a.g yes 1
20.d odd 2 1 3150.2.a.bh 1
20.e even 4 2 3150.2.g.b 2
28.d even 2 1 4410.2.a.a 1
60.h even 2 1 3150.2.a.s 1
60.l odd 4 2 3150.2.g.s 2
84.h odd 2 1 4410.2.a.bl 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.a.e 1 4.b odd 2 1
630.2.a.g yes 1 12.b even 2 1
3150.2.a.s 1 60.h even 2 1
3150.2.a.bh 1 20.d odd 2 1
3150.2.g.b 2 20.e even 4 2
3150.2.g.s 2 60.l odd 4 2
4410.2.a.a 1 28.d even 2 1
4410.2.a.bl 1 84.h odd 2 1
5040.2.a.n 1 3.b odd 2 1
5040.2.a.bp 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5040))\):

\( T_{11} - 4 \)
\( T_{13} - 6 \)
\( T_{17} - 4 \)
\( T_{19} + 6 \)
\( T_{29} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( -4 + T \)
$13$ \( -6 + T \)
$17$ \( -4 + T \)
$19$ \( 6 + T \)
$23$ \( T \)
$29$ \( 6 + T \)
$31$ \( -4 + T \)
$37$ \( -8 + T \)
$41$ \( -10 + T \)
$43$ \( -2 + T \)
$47$ \( 10 + T \)
$53$ \( -14 + T \)
$59$ \( -4 + T \)
$61$ \( 8 + T \)
$67$ \( 6 + T \)
$71$ \( -2 + T \)
$73$ \( 10 + T \)
$79$ \( 16 + T \)
$83$ \( -8 + T \)
$89$ \( -2 + T \)
$97$ \( -2 + T \)
show more
show less