Properties

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

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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

\(f(q)\) \(=\) \( q - q^{5} + O(q^{10}) \) \( q - q^{5} + 5q^{11} - 2q^{13} + 6q^{17} + 2q^{19} - 6q^{23} - 4q^{25} + 3q^{29} + 5q^{31} - 2q^{37} + 8q^{41} + 4q^{43} - 4q^{47} - 9q^{53} - 5q^{55} + 3q^{59} + 12q^{61} + 2q^{65} - 2q^{67} - 8q^{71} + 14q^{73} - q^{79} - 17q^{83} - 6q^{85} + 18q^{89} - 2q^{95} - 3q^{97} + O(q^{100}) \)

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 −1.00000 0 0 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 7056.2.a.v 1
3.b odd 2 1 7056.2.a.bh 1
4.b odd 2 1 3528.2.a.h 1
7.b odd 2 1 7056.2.a.bm 1
7.d odd 6 2 1008.2.s.h 2
12.b even 2 1 3528.2.a.s 1
21.c even 2 1 7056.2.a.r 1
21.g even 6 2 1008.2.s.l 2
28.d even 2 1 3528.2.a.o 1
28.f even 6 2 504.2.s.b 2
28.g odd 6 2 3528.2.s.r 2
84.h odd 2 1 3528.2.a.l 1
84.j odd 6 2 504.2.s.f yes 2
84.n even 6 2 3528.2.s.l 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
504.2.s.b 2 28.f even 6 2
504.2.s.f yes 2 84.j odd 6 2
1008.2.s.h 2 7.d odd 6 2
1008.2.s.l 2 21.g even 6 2
3528.2.a.h 1 4.b odd 2 1
3528.2.a.l 1 84.h odd 2 1
3528.2.a.o 1 28.d even 2 1
3528.2.a.s 1 12.b even 2 1
3528.2.s.l 2 84.n even 6 2
3528.2.s.r 2 28.g odd 6 2
7056.2.a.r 1 21.c even 2 1
7056.2.a.v 1 1.a even 1 1 trivial
7056.2.a.bh 1 3.b odd 2 1
7056.2.a.bm 1 7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\):

\( T_{5} + 1 \)
\( T_{11} - 5 \)
\( T_{13} + 2 \)
\( T_{17} - 6 \)
\( T_{23} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 + T + 5 T^{2} \)
$7$ 1
$11$ \( 1 - 5 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - 6 T + 17 T^{2} \)
$19$ \( 1 - 2 T + 19 T^{2} \)
$23$ \( 1 + 6 T + 23 T^{2} \)
$29$ \( 1 - 3 T + 29 T^{2} \)
$31$ \( 1 - 5 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 - 8 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 4 T + 47 T^{2} \)
$53$ \( 1 + 9 T + 53 T^{2} \)
$59$ \( 1 - 3 T + 59 T^{2} \)
$61$ \( 1 - 12 T + 61 T^{2} \)
$67$ \( 1 + 2 T + 67 T^{2} \)
$71$ \( 1 + 8 T + 71 T^{2} \)
$73$ \( 1 - 14 T + 73 T^{2} \)
$79$ \( 1 + T + 79 T^{2} \)
$83$ \( 1 + 17 T + 83 T^{2} \)
$89$ \( 1 - 18 T + 89 T^{2} \)
$97$ \( 1 + 3 T + 97 T^{2} \)
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