Properties

Label 8016.2.a.d
Level $8016$
Weight $2$
Character orbit 8016.a
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{3} - 4q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - 4q^{7} + q^{9} + 4q^{11} + 2q^{13} + 4q^{19} + 4q^{21} - 5q^{25} - q^{27} + 6q^{29} - 8q^{31} - 4q^{33} + 6q^{37} - 2q^{39} - 2q^{43} - 8q^{47} + 9q^{49} + 8q^{53} - 4q^{57} + 10q^{61} - 4q^{63} - 14q^{67} + 12q^{71} - 2q^{73} + 5q^{75} - 16q^{77} - 2q^{79} + q^{81} + 12q^{83} - 6q^{87} - 6q^{89} - 8q^{91} + 8q^{93} - 6q^{97} + 4q^{99} + O(q^{100}) \)

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 0 0 −4.00000 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.d 1
4.b odd 2 1 4008.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4008.2.a.d 1 4.b odd 2 1
8016.2.a.d 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8016))\):

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

Hecke characteristic polynomials

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