Properties

Label 7056.2.a.by
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 126)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3q^{5} + O(q^{10}) \) \( q + 3q^{5} + 3q^{11} + 2q^{13} + 6q^{17} - 2q^{19} + 6q^{23} + 4q^{25} + 9q^{29} + 7q^{31} - 10q^{37} + 4q^{43} - 12q^{47} - 3q^{53} + 9q^{55} + 3q^{59} - 4q^{61} + 6q^{65} - 2q^{67} + 2q^{73} - 5q^{79} - 9q^{83} + 18q^{85} - 6q^{89} - 6q^{95} - 13q^{97} + O(q^{100}) \)

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 3.00000 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.by 1
3.b odd 2 1 7056.2.a.e 1
4.b odd 2 1 882.2.a.j 1
7.b odd 2 1 7056.2.a.h 1
7.c even 3 2 1008.2.s.b 2
12.b even 2 1 882.2.a.a 1
21.c even 2 1 7056.2.a.bx 1
21.h odd 6 2 1008.2.s.o 2
28.d even 2 1 882.2.a.h 1
28.f even 6 2 882.2.g.e 2
28.g odd 6 2 126.2.g.a 2
84.h odd 2 1 882.2.a.e 1
84.j odd 6 2 882.2.g.g 2
84.n even 6 2 126.2.g.d yes 2
252.o even 6 2 1134.2.h.j 2
252.u odd 6 2 1134.2.e.k 2
252.bb even 6 2 1134.2.e.g 2
252.bl odd 6 2 1134.2.h.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.g.a 2 28.g odd 6 2
126.2.g.d yes 2 84.n even 6 2
882.2.a.a 1 12.b even 2 1
882.2.a.e 1 84.h odd 2 1
882.2.a.h 1 28.d even 2 1
882.2.a.j 1 4.b odd 2 1
882.2.g.e 2 28.f even 6 2
882.2.g.g 2 84.j odd 6 2
1008.2.s.b 2 7.c even 3 2
1008.2.s.o 2 21.h odd 6 2
1134.2.e.g 2 252.bb even 6 2
1134.2.e.k 2 252.u odd 6 2
1134.2.h.f 2 252.bl odd 6 2
1134.2.h.j 2 252.o even 6 2
7056.2.a.e 1 3.b odd 2 1
7056.2.a.h 1 7.b odd 2 1
7056.2.a.bx 1 21.c even 2 1
7056.2.a.by 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\):

\( T_{5} - 3 \)
\( T_{11} - 3 \)
\( T_{13} - 2 \)
\( T_{17} - 6 \)
\( T_{23} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 - 3 T + 5 T^{2} \)
$7$ 1
$11$ \( 1 - 3 T + 11 T^{2} \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 - 6 T + 17 T^{2} \)
$19$ \( 1 + 2 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 - 9 T + 29 T^{2} \)
$31$ \( 1 - 7 T + 31 T^{2} \)
$37$ \( 1 + 10 T + 37 T^{2} \)
$41$ \( 1 + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 12 T + 47 T^{2} \)
$53$ \( 1 + 3 T + 53 T^{2} \)
$59$ \( 1 - 3 T + 59 T^{2} \)
$61$ \( 1 + 4 T + 61 T^{2} \)
$67$ \( 1 + 2 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 - 2 T + 73 T^{2} \)
$79$ \( 1 + 5 T + 79 T^{2} \)
$83$ \( 1 + 9 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 + 13 T + 97 T^{2} \)
show more
show less