Properties

Label 6160.2.a.q
Level $6160$
Weight $2$
Character orbit 6160.a
Self dual yes
Analytic conductor $49.188$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.1878476451\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3080)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{3} + q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q + 2 q^{3} + q^{5} + q^{7} + q^{9} + q^{11} + 6 q^{13} + 2 q^{15} + 2 q^{17} - 2 q^{19} + 2 q^{21} + 6 q^{23} + q^{25} - 4 q^{27} + 2 q^{33} + q^{35} - 4 q^{37} + 12 q^{39} - 8 q^{41} + 4 q^{43} + q^{45} + 4 q^{47} + q^{49} + 4 q^{51} + 8 q^{53} + q^{55} - 4 q^{57} + 4 q^{59} + 14 q^{61} + q^{63} + 6 q^{65} - 8 q^{67} + 12 q^{69} - 12 q^{71} + 2 q^{73} + 2 q^{75} + q^{77} - 6 q^{79} - 11 q^{81} + 2 q^{85} - 2 q^{89} + 6 q^{91} - 2 q^{95} + 12 q^{97} + q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

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 6160.2.a.q 1
4.b odd 2 1 3080.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3080.2.a.b 1 4.b odd 2 1
6160.2.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6160))\):

\( T_{3} - 2 \)
\( T_{13} - 6 \)
\( T_{17} - 2 \)
\( T_{19} + 2 \)
\( T_{23} - 6 \)

Hecke characteristic polynomials

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