Properties

Label 2016.2.a.l
Level $2016$
Weight $2$
Character orbit 2016.a
Self dual yes
Analytic conductor $16.098$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.0978410475\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 672)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{5} + q^{7} + O(q^{10}) \) \( q + 2q^{5} + q^{7} - 4q^{11} - 6q^{13} + 2q^{17} - 4q^{19} - 4q^{23} - q^{25} + 2q^{29} - 8q^{31} + 2q^{35} - 10q^{37} + 2q^{41} - 8q^{43} + q^{49} + 10q^{53} - 8q^{55} - 12q^{59} + 10q^{61} - 12q^{65} + 8q^{67} + 12q^{71} + 2q^{73} - 4q^{77} + 12q^{83} + 4q^{85} - 6q^{89} - 6q^{91} - 8q^{95} + 2q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(7\) \(-1\)

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 2016.2.a.l 1
3.b odd 2 1 672.2.a.b 1
4.b odd 2 1 2016.2.a.k 1
8.b even 2 1 4032.2.a.n 1
8.d odd 2 1 4032.2.a.f 1
12.b even 2 1 672.2.a.f yes 1
21.c even 2 1 4704.2.a.be 1
24.f even 2 1 1344.2.a.h 1
24.h odd 2 1 1344.2.a.r 1
48.i odd 4 2 5376.2.c.m 2
48.k even 4 2 5376.2.c.s 2
84.h odd 2 1 4704.2.a.m 1
168.e odd 2 1 9408.2.a.cb 1
168.i even 2 1 9408.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
672.2.a.b 1 3.b odd 2 1
672.2.a.f yes 1 12.b even 2 1
1344.2.a.h 1 24.f even 2 1
1344.2.a.r 1 24.h odd 2 1
2016.2.a.k 1 4.b odd 2 1
2016.2.a.l 1 1.a even 1 1 trivial
4032.2.a.f 1 8.d odd 2 1
4032.2.a.n 1 8.b even 2 1
4704.2.a.m 1 84.h odd 2 1
4704.2.a.be 1 21.c even 2 1
5376.2.c.m 2 48.i odd 4 2
5376.2.c.s 2 48.k even 4 2
9408.2.a.g 1 168.i even 2 1
9408.2.a.cb 1 168.e odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2016))\):

\( T_{5} - 2 \)
\( T_{11} + 4 \)
\( T_{13} + 6 \)
\( T_{17} - 2 \)
\( T_{19} + 4 \)

Hecke characteristic polynomials

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