Properties

Label 2016.4.a.e
Level $2016$
Weight $4$
Character orbit 2016.a
Self dual yes
Analytic conductor $118.948$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(118.947850572\)
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

\(f(q)\) \(=\) \( q + 18q^{5} - 7q^{7} + O(q^{10}) \) \( q + 18q^{5} - 7q^{7} - 44q^{11} + 58q^{13} + 130q^{17} + 92q^{19} - 84q^{23} + 199q^{25} + 250q^{29} - 72q^{31} - 126q^{35} - 354q^{37} - 334q^{41} - 416q^{43} + 464q^{47} + 49q^{49} + 450q^{53} - 792q^{55} + 516q^{59} + 58q^{61} + 1044q^{65} - 656q^{67} + 940q^{71} + 178q^{73} + 308q^{77} + 1072q^{79} - 660q^{83} + 2340q^{85} - 1254q^{89} - 406q^{91} + 1656q^{95} + 210q^{97} + O(q^{100}) \)

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 18.0000 0 −7.00000 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 2016.4.a.e 1
3.b odd 2 1 672.4.a.c yes 1
4.b odd 2 1 2016.4.a.f 1
12.b even 2 1 672.4.a.a 1
24.f even 2 1 1344.4.a.bb 1
24.h odd 2 1 1344.4.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
672.4.a.a 1 12.b even 2 1
672.4.a.c yes 1 3.b odd 2 1
1344.4.a.m 1 24.h odd 2 1
1344.4.a.bb 1 24.f even 2 1
2016.4.a.e 1 1.a even 1 1 trivial
2016.4.a.f 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2016))\):

\( T_{5} - 18 \)
\( T_{11} + 44 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -18 + T \)
$7$ \( 7 + T \)
$11$ \( 44 + T \)
$13$ \( -58 + T \)
$17$ \( -130 + T \)
$19$ \( -92 + T \)
$23$ \( 84 + T \)
$29$ \( -250 + T \)
$31$ \( 72 + T \)
$37$ \( 354 + T \)
$41$ \( 334 + T \)
$43$ \( 416 + T \)
$47$ \( -464 + T \)
$53$ \( -450 + T \)
$59$ \( -516 + T \)
$61$ \( -58 + T \)
$67$ \( 656 + T \)
$71$ \( -940 + T \)
$73$ \( -178 + T \)
$79$ \( -1072 + T \)
$83$ \( 660 + T \)
$89$ \( 1254 + T \)
$97$ \( -210 + T \)
show more
show less