Newform orbit 560.3.v.a

• Label: 560.3.v.a
• Level: $560$
• Weight: $3$
• Character orbit: 560.v
• Analytic conductor: $15.259$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.2588948042\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 64 q^{21} + 72 q^{25} - 72 q^{37} - 272 q^{53} + 280 q^{57} + 376 q^{65} + 24 q^{77} - 528 q^{81} - 96 q^{85} - 552 q^{93}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
223.1		0		−3.74578	−	3.74578i		0		−3.76482	−	3.29031i		0		6.99995	+	0.0261022i		0				19.0618i		0
223.2		0		−3.74578	−	3.74578i		0		3.76482	+	3.29031i		0		−0.0261022	−	6.99995i		0				19.0618i		0
223.3		0		−2.85574	−	2.85574i		0		−3.59158	+	3.47858i		0		−6.44957	+	2.72085i		0				7.31049i		0
223.4		0		−2.85574	−	2.85574i		0		3.59158	−	3.47858i		0		−2.72085	+	6.44957i		0				7.31049i		0
223.5		0		−1.21355	−	1.21355i		0		−4.89142	+	1.03636i		0		2.17441	−	6.65372i		0			−	6.05460i		0
223.6		0		−1.21355	−	1.21355i		0		4.89142	−	1.03636i		0		6.65372	−	2.17441i		0			−	6.05460i		0
223.7		0		−0.917157	−	0.917157i		0		1.87103	+	4.63673i		0		3.29129	+	6.17798i		0			−	7.31765i		0
223.8		0		−0.917157	−	0.917157i		0		−1.87103	−	4.63673i		0		−6.17798	−	3.29129i		0			−	7.31765i		0
223.9		0		0.917157	+	0.917157i		0		−1.87103	−	4.63673i		0		6.17798	+	3.29129i		0			−	7.31765i		0
223.10		0		0.917157	+	0.917157i		0		1.87103	+	4.63673i		0		−3.29129	−	6.17798i		0			−	7.31765i		0
223.11		0		1.21355	+	1.21355i		0		4.89142	−	1.03636i		0		−6.65372	+	2.17441i		0			−	6.05460i		0
223.12		0		1.21355	+	1.21355i		0		−4.89142	+	1.03636i		0		−2.17441	+	6.65372i		0			−	6.05460i		0
223.13		0		2.85574	+	2.85574i		0		3.59158	−	3.47858i		0		2.72085	−	6.44957i		0				7.31049i		0
223.14		0		2.85574	+	2.85574i		0		−3.59158	+	3.47858i		0		6.44957	−	2.72085i		0				7.31049i		0
223.15		0		3.74578	+	3.74578i		0		3.76482	+	3.29031i		0		0.0261022	+	6.99995i		0				19.0618i		0
223.16		0		3.74578	+	3.74578i		0		−3.76482	−	3.29031i		0		−6.99995	−	0.0261022i		0				19.0618i		0
447.1		0		−3.74578	+	3.74578i		0		−3.76482	+	3.29031i		0		6.99995	−	0.0261022i		0			−	19.0618i		0
447.2		0		−3.74578	+	3.74578i		0		3.76482	−	3.29031i		0		−0.0261022	+	6.99995i		0			−	19.0618i		0
447.3		0		−2.85574	+	2.85574i		0		−3.59158	−	3.47858i		0		−6.44957	−	2.72085i		0			−	7.31049i		0
447.4		0		−2.85574	+	2.85574i		0		3.59158	+	3.47858i		0		−2.72085	−	6.44957i		0			−	7.31049i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.c	odd	4	1	inner
7.b	odd	2	1	inner
20.e	even	4	1	inner
28.d	even	2	1	inner
35.f	even	4	1	inner
140.j	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	560.3.v.a	✓	32
4.b	odd	2	1	inner	560.3.v.a	✓	32
5.c	odd	4	1	inner	560.3.v.a	✓	32
7.b	odd	2	1	inner	560.3.v.a	✓	32
20.e	even	4	1	inner	560.3.v.a	✓	32
28.d	even	2	1	inner	560.3.v.a	✓	32
35.f	even	4	1	inner	560.3.v.a	✓	32
140.j	odd	4	1	inner	560.3.v.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
560.3.v.a	✓	32	1.a	even	1	1	trivial
560.3.v.a	✓	32	4.b	odd	2	1	inner
560.3.v.a	✓	32	5.c	odd	4	1	inner
560.3.v.a	✓	32	7.b	odd	2	1	inner
560.3.v.a	✓	32	20.e	even	4	1	inner
560.3.v.a	✓	32	28.d	even	2	1	inner
560.3.v.a	✓	32	35.f	even	4	1	inner
560.3.v.a	✓	32	140.j	odd	4	1	inner