Properties

Label 7056.2.a.bt
Level 7056
Weight 2
Character orbit 7056.a
Self dual yes
Analytic conductor 56.342
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.3424436662\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{5} + O(q^{10}) \) \( q + 2q^{5} + 2q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + 6q^{23} - q^{25} - 4q^{31} + 10q^{37} + 2q^{41} + 4q^{43} - 4q^{47} + 12q^{53} + 4q^{55} - 12q^{59} - 6q^{61} - 4q^{65} + 4q^{67} - 14q^{71} + 2q^{73} + 8q^{79} + 16q^{83} + 12q^{85} - 6q^{89} - 8q^{95} + 18q^{97} + O(q^{100}) \)

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

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 7056.2.a.bt 1
3.b odd 2 1 7056.2.a.l 1
4.b odd 2 1 3528.2.a.u 1
7.b odd 2 1 1008.2.a.f 1
12.b even 2 1 3528.2.a.e 1
21.c even 2 1 1008.2.a.k 1
28.d even 2 1 504.2.a.a 1
28.f even 6 2 3528.2.s.x 2
28.g odd 6 2 3528.2.s.i 2
56.e even 2 1 4032.2.a.bf 1
56.h odd 2 1 4032.2.a.bg 1
84.h odd 2 1 504.2.a.f yes 1
84.j odd 6 2 3528.2.s.f 2
84.n even 6 2 3528.2.s.u 2
168.e odd 2 1 4032.2.a.g 1
168.i even 2 1 4032.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
504.2.a.a 1 28.d even 2 1
504.2.a.f yes 1 84.h odd 2 1
1008.2.a.f 1 7.b odd 2 1
1008.2.a.k 1 21.c even 2 1
3528.2.a.e 1 12.b even 2 1
3528.2.a.u 1 4.b odd 2 1
3528.2.s.f 2 84.j odd 6 2
3528.2.s.i 2 28.g odd 6 2
3528.2.s.u 2 84.n even 6 2
3528.2.s.x 2 28.f even 6 2
4032.2.a.g 1 168.e odd 2 1
4032.2.a.l 1 168.i even 2 1
4032.2.a.bf 1 56.e even 2 1
4032.2.a.bg 1 56.h odd 2 1
7056.2.a.l 1 3.b odd 2 1
7056.2.a.bt 1 1.a even 1 1 trivial

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\):

\( T_{5} - 2 \)
\( T_{11} - 2 \)
\( T_{13} + 2 \)
\( T_{17} - 6 \)
\( T_{23} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 - 2 T + 5 T^{2} \)
$7$ 1
$11$ \( 1 - 2 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - 6 T + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 - 10 T + 37 T^{2} \)
$41$ \( 1 - 2 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 4 T + 47 T^{2} \)
$53$ \( 1 - 12 T + 53 T^{2} \)
$59$ \( 1 + 12 T + 59 T^{2} \)
$61$ \( 1 + 6 T + 61 T^{2} \)
$67$ \( 1 - 4 T + 67 T^{2} \)
$71$ \( 1 + 14 T + 71 T^{2} \)
$73$ \( 1 - 2 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 - 16 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 18 T + 97 T^{2} \)
show more
show less