Properties

Label 7920.2.a.m
Level $7920$
Weight $2$
Character orbit 7920.a
Self dual yes
Analytic conductor $63.242$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 330)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} + O(q^{10}) \) \( q - q^{5} + q^{11} + 6q^{13} - 2q^{17} + 4q^{19} + q^{25} + 10q^{29} + 6q^{37} - 2q^{41} - 4q^{43} - 8q^{47} - 7q^{49} + 10q^{53} - q^{55} - 4q^{59} - 2q^{61} - 6q^{65} + 4q^{67} - 8q^{71} + 2q^{73} + 8q^{79} - 12q^{83} + 2q^{85} + 6q^{89} - 4q^{95} + 18q^{97} + O(q^{100}) \)

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

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.m 1
3.b odd 2 1 2640.2.a.t 1
4.b odd 2 1 990.2.a.b 1
12.b even 2 1 330.2.a.d 1
20.d odd 2 1 4950.2.a.bg 1
20.e even 4 2 4950.2.c.j 2
60.h even 2 1 1650.2.a.h 1
60.l odd 4 2 1650.2.c.g 2
132.d odd 2 1 3630.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
330.2.a.d 1 12.b even 2 1
990.2.a.b 1 4.b odd 2 1
1650.2.a.h 1 60.h even 2 1
1650.2.c.g 2 60.l odd 4 2
2640.2.a.t 1 3.b odd 2 1
3630.2.a.f 1 132.d odd 2 1
4950.2.a.bg 1 20.d odd 2 1
4950.2.c.j 2 20.e even 4 2
7920.2.a.m 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7920))\):

\( T_{7} \)
\( T_{13} - 6 \)
\( T_{17} + 2 \)
\( T_{19} - 4 \)
\( T_{23} \)
\( T_{29} - 10 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( -1 + T \)
$13$ \( -6 + T \)
$17$ \( 2 + T \)
$19$ \( -4 + T \)
$23$ \( T \)
$29$ \( -10 + T \)
$31$ \( T \)
$37$ \( -6 + T \)
$41$ \( 2 + T \)
$43$ \( 4 + T \)
$47$ \( 8 + T \)
$53$ \( -10 + T \)
$59$ \( 4 + T \)
$61$ \( 2 + T \)
$67$ \( -4 + T \)
$71$ \( 8 + T \)
$73$ \( -2 + T \)
$79$ \( -8 + T \)
$83$ \( 12 + T \)
$89$ \( -6 + T \)
$97$ \( -18 + T \)
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