Newform orbit 5760.2.a.f

• Label: 5760.2.a.f
• Level: $5760$
• Weight: $2$
• Character orbit: 5760.a
• Self dual: yes
• Analytic conductor: $45.994$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$5760 = 2^{7} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	5760.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$45.9938315643$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 1920)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - q^5 - 2 * q^7 + 2 * q^11 - 6 * q^13 + 6 * q^17 + 6 * q^19 - 2 * q^23 + q^25 + 2 * q^29 - 4 * q^31 + 2 * q^35 - 10 * q^37 + 2 * q^41 - 8 * q^43 + 6 * q^47 - 3 * q^49 + 6 * q^53 - 2 * q^55 - 10 * q^59 + 14 * q^61 + 6 * q^65 + 8 * q^67 + 8 * q^71 + 2 * q^73 - 4 * q^77 - 12 * q^83 - 6 * q^85 + 10 * q^89 + 12 * q^91 - 6 * q^95 - 6 * 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

−1.00000

0

−2.00000

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$5$	$+1$

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	5760.2.a.f		1
3.b	odd	2	1		1920.2.a.t	yes	1
4.b	odd	2	1		5760.2.a.r		1
8.b	even	2	1		5760.2.a.bc		1
8.d	odd	2	1		5760.2.a.bs		1
12.b	even	2	1		1920.2.a.k	yes	1
15.d	odd	2	1		9600.2.a.u		1
24.f	even	2	1		1920.2.a.p	yes	1
24.h	odd	2	1		1920.2.a.c	✓	1
48.i	odd	4	2		3840.2.k.u		2
48.k	even	4	2		3840.2.k.g		2
60.h	even	2	1		9600.2.a.bj		1
120.i	odd	2	1		9600.2.a.by		1
120.m	even	2	1		9600.2.a.f		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1920.2.a.c	✓	1	24.h	odd	2	1
1920.2.a.k	yes	1	12.b	even	2	1
1920.2.a.p	yes	1	24.f	even	2	1
1920.2.a.t	yes	1	3.b	odd	2	1
3840.2.k.g		2	48.k	even	4	2
3840.2.k.u		2	48.i	odd	4	2
5760.2.a.f		1	1.a	even	1	1	trivial
5760.2.a.r		1	4.b	odd	2	1
5760.2.a.bc		1	8.b	even	2	1
5760.2.a.bs		1	8.d	odd	2	1
9600.2.a.f		1	120.m	even	2	1
9600.2.a.u		1	15.d	odd	2	1
9600.2.a.bj		1	60.h	even	2	1
9600.2.a.by		1	120.i	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(5760))$:

$T_{7} + 2$

$T_{11} - 2$

$T_{13} + 6$

$T_{17} - 6$

$T_{29} - 2$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 1$
$7$	$T + 2$
$11$	$T - 2$