Properties

Label 2016.2.a.a
Level $2016$
Weight $2$
Character orbit 2016.a
Self dual yes
Analytic conductor $16.098$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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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: \(0\)
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

\(f(q)\) \(=\) \( q - 2q^{5} - q^{7} + O(q^{10}) \) \( q - 2q^{5} - q^{7} + 2q^{13} - 2q^{17} + 4q^{19} - q^{25} - 6q^{29} + 2q^{35} + 6q^{37} + 6q^{41} + 8q^{43} - 8q^{47} + q^{49} - 6q^{53} + 12q^{59} + 10q^{61} - 4q^{65} + 16q^{67} + 8q^{71} - 6q^{73} + 8q^{79} + 12q^{83} + 4q^{85} + 14q^{89} - 2q^{91} - 8q^{95} - 6q^{97} + O(q^{100}) \)

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.a 1
3.b odd 2 1 672.2.a.d 1
4.b odd 2 1 2016.2.a.b 1
8.b even 2 1 4032.2.a.bd 1
8.d odd 2 1 4032.2.a.bi 1
12.b even 2 1 672.2.a.h yes 1
21.c even 2 1 4704.2.a.v 1
24.f even 2 1 1344.2.a.d 1
24.h odd 2 1 1344.2.a.l 1
48.i odd 4 2 5376.2.c.u 2
48.k even 4 2 5376.2.c.o 2
84.h odd 2 1 4704.2.a.c 1
168.e odd 2 1 9408.2.a.cz 1
168.i even 2 1 9408.2.a.bd 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
672.2.a.d 1 3.b odd 2 1
672.2.a.h yes 1 12.b even 2 1
1344.2.a.d 1 24.f even 2 1
1344.2.a.l 1 24.h odd 2 1
2016.2.a.a 1 1.a even 1 1 trivial
2016.2.a.b 1 4.b odd 2 1
4032.2.a.bd 1 8.b even 2 1
4032.2.a.bi 1 8.d odd 2 1
4704.2.a.c 1 84.h odd 2 1
4704.2.a.v 1 21.c even 2 1
5376.2.c.o 2 48.k even 4 2
5376.2.c.u 2 48.i odd 4 2
9408.2.a.bd 1 168.i even 2 1
9408.2.a.cz 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2016))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 + 2 T + 5 T^{2} \)
$7$ \( 1 + T \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 + 2 T + 17 T^{2} \)
$19$ \( 1 - 4 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 + 31 T^{2} \)
$37$ \( 1 - 6 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 - 8 T + 43 T^{2} \)
$47$ \( 1 + 8 T + 47 T^{2} \)
$53$ \( 1 + 6 T + 53 T^{2} \)
$59$ \( 1 - 12 T + 59 T^{2} \)
$61$ \( 1 - 10 T + 61 T^{2} \)
$67$ \( 1 - 16 T + 67 T^{2} \)
$71$ \( 1 - 8 T + 71 T^{2} \)
$73$ \( 1 + 6 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 - 12 T + 83 T^{2} \)
$89$ \( 1 - 14 T + 89 T^{2} \)
$97$ \( 1 + 6 T + 97 T^{2} \)
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