Newform orbit 2720.2.l.b

• Label: 2720.2.l.b
• Level: $2720$
• Weight: $2$
• Character orbit: 2720.l
• Analytic conductor: $21.719$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2720 = 2^{5} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2720.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(21.7193093498\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	no (minimal twist has level 680)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 4 q^{3} + 36 q^{5} + 36 q^{9} + 8 q^{11} + 4 q^{15} + 36 q^{25} + 16 q^{27} - 8 q^{33} + 36 q^{45} - 20 q^{47} - 36 q^{49} + 8 q^{55} + 4 q^{75} + 44 q^{81} - 24 q^{87} + 56 q^{91} + 40 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2481.1		0		−3.03317				0		1.00000				0			−	1.14609i		0		6.20011				0
2481.2		0		−3.03317				0		1.00000				0				1.14609i		0		6.20011				0
2481.3		0		−2.68470				0		1.00000				0				4.42201i		0		4.20759				0
2481.4		0		−2.68470				0		1.00000				0			−	4.42201i		0		4.20759				0
2481.5		0		−2.54711				0		1.00000				0				0.654431i		0		3.48778				0
2481.6		0		−2.54711				0		1.00000				0			−	0.654431i		0		3.48778				0
2481.7		0		−2.32748				0		1.00000				0			−	1.14286i		0		2.41716				0
2481.8		0		−2.32748				0		1.00000				0				1.14286i		0		2.41716				0
2481.9		0		−1.52644				0		1.00000				0			−	2.26675i		0		−0.669989				0
2481.10		0		−1.52644				0		1.00000				0				2.26675i		0		−0.669989				0
2481.11		0		−1.30568				0		1.00000				0				5.06709i		0		−1.29519				0
2481.12		0		−1.30568				0		1.00000				0			−	5.06709i		0		−1.29519				0
2481.13		0		−0.904376				0		1.00000				0				1.75754i		0		−2.18210				0
2481.14		0		−0.904376				0		1.00000				0			−	1.75754i		0		−2.18210				0
2481.15		0		−0.228800				0		1.00000				0			−	3.99056i		0		−2.94765				0
2481.16		0		−0.228800				0		1.00000				0				3.99056i		0		−2.94765				0
2481.17		0		0.0722782				0		1.00000				0				0.600402i		0		−2.99478				0
2481.18		0		0.0722782				0		1.00000				0			−	0.600402i		0		−2.99478				0
2481.19		0		0.528085				0		1.00000				0				4.36555i		0		−2.72113				0
2481.20		0		0.528085				0		1.00000				0			−	4.36555i		0		−2.72113				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
136.h	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2720.2.l.b		36
4.b	odd	2	1		680.2.l.a	✓	36
8.b	even	2	1		2720.2.l.a		36
8.d	odd	2	1		680.2.l.b	yes	36
17.b	even	2	1		2720.2.l.a		36
68.d	odd	2	1		680.2.l.b	yes	36
136.e	odd	2	1		680.2.l.a	✓	36
136.h	even	2	1	inner	2720.2.l.b		36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
680.2.l.a	✓	36	4.b	odd	2	1
680.2.l.a	✓	36	136.e	odd	2	1
680.2.l.b	yes	36	8.d	odd	2	1
680.2.l.b	yes	36	68.d	odd	2	1
2720.2.l.a		36	8.b	even	2	1
2720.2.l.a		36	17.b	even	2	1
2720.2.l.b		36	1.a	even	1	1	trivial
2720.2.l.b		36	136.h	even	2	1	inner