Newform orbit 7056.2.a.n

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

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 588)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 2 * q^5 + 2 * q^11 - 4 * q^13 - 6 * q^17 - 8 * q^19 - 6 * q^23 - q^25 + 10 * q^29 - 4 * q^31 + 6 * q^37 + 6 * q^41 - 4 * q^43 + 8 * q^47 - 2 * q^53 - 4 * q^55 - 4 * q^59 - 8 * q^61 + 8 * q^65 + 8 * q^67 - 10 * q^71 + 4 * q^73 - 4 * q^79 + 12 * q^83 + 12 * q^85 + 14 * q^89 + 16 * q^95 + 4 * q^97

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

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.n		1
3.b	odd	2	1		2352.2.a.j		1
4.b	odd	2	1		1764.2.a.b		1
7.b	odd	2	1		7056.2.a.bu		1
12.b	even	2	1		588.2.a.e	yes	1
21.c	even	2	1		2352.2.a.p		1
21.g	even	6	2		2352.2.q.k		2
21.h	odd	6	2		2352.2.q.p		2
24.f	even	2	1		9408.2.a.l		1
24.h	odd	2	1		9408.2.a.ca		1
28.d	even	2	1		1764.2.a.i		1
28.f	even	6	2		1764.2.k.c		2
28.g	odd	6	2		1764.2.k.i		2
84.h	odd	2	1		588.2.a.b	✓	1
84.j	odd	6	2		588.2.i.g		2
84.n	even	6	2		588.2.i.a		2
168.e	odd	2	1		9408.2.a.cu		1
168.i	even	2	1		9408.2.a.bf		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
588.2.a.b	✓	1	84.h	odd	2	1
588.2.a.e	yes	1	12.b	even	2	1
588.2.i.a		2	84.n	even	6	2
588.2.i.g		2	84.j	odd	6	2
1764.2.a.b		1	4.b	odd	2	1
1764.2.a.i		1	28.d	even	2	1
1764.2.k.c		2	28.f	even	6	2
1764.2.k.i		2	28.g	odd	6	2
2352.2.a.j		1	3.b	odd	2	1
2352.2.a.p		1	21.c	even	2	1
2352.2.q.k		2	21.g	even	6	2
2352.2.q.p		2	21.h	odd	6	2
7056.2.a.n		1	1.a	even	1	1	trivial
7056.2.a.bu		1	7.b	odd	2	1
9408.2.a.l		1	24.f	even	2	1
9408.2.a.bf		1	168.i	even	2	1
9408.2.a.ca		1	24.h	odd	2	1
9408.2.a.cu		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 $S_{2}^{\mathrm{new}}(\Gamma_0(7056))$:

$T_{5} + 2$

$T_{11} - 2$

$T_{13} + 4$

$T_{17} + 6$

$T_{23} + 6$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 2$
$7$	$T$
$11$	$T - 2$