Properties

Label 8016.2.a.i
Level $8016$
Weight $2$
Character orbit 8016.a
Self dual yes
Analytic conductor $64.008$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{5} + 3q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} + q^{5} + 3q^{7} + q^{9} - 4q^{11} + 2q^{13} + q^{15} - 6q^{17} - 2q^{19} + 3q^{21} - 6q^{23} - 4q^{25} + q^{27} + 3q^{31} - 4q^{33} + 3q^{35} + 7q^{37} + 2q^{39} - 6q^{41} - 12q^{43} + q^{45} - 3q^{47} + 2q^{49} - 6q^{51} - 9q^{53} - 4q^{55} - 2q^{57} - 11q^{59} + 3q^{63} + 2q^{65} + 5q^{67} - 6q^{69} + 14q^{71} + 4q^{73} - 4q^{75} - 12q^{77} + q^{81} - 9q^{83} - 6q^{85} - 13q^{89} + 6q^{91} + 3q^{93} - 2q^{95} - q^{97} - 4q^{99} + O(q^{100}) \)

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 1.00000 0 1.00000 0 3.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(167\) \(-1\)

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 8016.2.a.i 1
4.b odd 2 1 4008.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4008.2.a.a 1 4.b odd 2 1
8016.2.a.i 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8016))\):

\( T_{5} - 1 \)
\( T_{7} - 3 \)
\( T_{11} + 4 \)
\( T_{13} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( -3 + T \)
$11$ \( 4 + T \)
$13$ \( -2 + T \)
$17$ \( 6 + T \)
$19$ \( 2 + T \)
$23$ \( 6 + T \)
$29$ \( T \)
$31$ \( -3 + T \)
$37$ \( -7 + T \)
$41$ \( 6 + T \)
$43$ \( 12 + T \)
$47$ \( 3 + T \)
$53$ \( 9 + T \)
$59$ \( 11 + T \)
$61$ \( T \)
$67$ \( -5 + T \)
$71$ \( -14 + T \)
$73$ \( -4 + T \)
$79$ \( T \)
$83$ \( 9 + T \)
$89$ \( 13 + T \)
$97$ \( 1 + T \)
show more
show less