Properties

Label 7920.2.a.be
Level $7920$
Weight $2$
Character orbit 7920.a
Self dual yes
Analytic conductor $63.242$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.2415184009\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1320)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5} + 2q^{7} + O(q^{10}) \) \( q + q^{5} + 2q^{7} - q^{11} - 4q^{13} + 4q^{17} - 8q^{19} + 4q^{23} + q^{25} - 2q^{29} - 8q^{31} + 2q^{35} - 2q^{37} + 2q^{41} + 6q^{43} + 12q^{47} - 3q^{49} - 6q^{53} - q^{55} - 12q^{59} + 10q^{61} - 4q^{65} - 16q^{67} + 4q^{73} - 2q^{77} - 12q^{79} - 6q^{83} + 4q^{85} - 6q^{89} - 8q^{91} - 8q^{95} + 14q^{97} + O(q^{100}) \)

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
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(11\) \(1\)

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 7920.2.a.be 1
3.b odd 2 1 2640.2.a.p 1
4.b odd 2 1 3960.2.a.n 1
12.b even 2 1 1320.2.a.a 1
60.h even 2 1 6600.2.a.bb 1
60.l odd 4 2 6600.2.d.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1320.2.a.a 1 12.b even 2 1
2640.2.a.p 1 3.b odd 2 1
3960.2.a.n 1 4.b odd 2 1
6600.2.a.bb 1 60.h even 2 1
6600.2.d.a 2 60.l odd 4 2
7920.2.a.be 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7920))\):

\( T_{7} - 2 \)
\( T_{13} + 4 \)
\( T_{17} - 4 \)
\( T_{19} + 8 \)
\( T_{23} - 4 \)
\( T_{29} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( -2 + T \)
$11$ \( 1 + T \)
$13$ \( 4 + T \)
$17$ \( -4 + T \)
$19$ \( 8 + T \)
$23$ \( -4 + T \)
$29$ \( 2 + T \)
$31$ \( 8 + T \)
$37$ \( 2 + T \)
$41$ \( -2 + T \)
$43$ \( -6 + T \)
$47$ \( -12 + T \)
$53$ \( 6 + T \)
$59$ \( 12 + T \)
$61$ \( -10 + T \)
$67$ \( 16 + T \)
$71$ \( T \)
$73$ \( -4 + T \)
$79$ \( 12 + T \)
$83$ \( 6 + T \)
$89$ \( 6 + T \)
$97$ \( -14 + T \)
show more
show less