Newform orbit 1120.2.l.a

• Label: 1120.2.l.a
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.l
• Analytic conductor: $8.943$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.94324502638\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	no (minimal twist has level 280)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 36 q^{9} + 4 q^{25} + 16 q^{31} + 32 q^{39} - 8 q^{41} - 36 q^{49} + 32 q^{55} - 24 q^{65} - 56 q^{71} - 24 q^{79} + 36 q^{81} - 40 q^{89} - 40 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1009.1		0		−3.10393				0		−0.0152300	+	2.23602i		0				1.00000i		0		6.63436				0
1009.2		0		−3.10393				0		−0.0152300	−	2.23602i		0			−	1.00000i		0		6.63436				0
1009.3		0		−2.96656				0		−2.18846	+	0.458941i		0			−	1.00000i		0		5.80046				0
1009.4		0		−2.96656				0		−2.18846	−	0.458941i		0				1.00000i		0		5.80046				0
1009.5		0		−2.55593				0		0.790907	+	2.09152i		0			−	1.00000i		0		3.53279				0
1009.6		0		−2.55593				0		0.790907	−	2.09152i		0				1.00000i		0		3.53279				0
1009.7		0		−2.12140				0		2.02293	+	0.952769i		0				1.00000i		0		1.50036				0
1009.8		0		−2.12140				0		2.02293	−	0.952769i		0			−	1.00000i		0		1.50036				0
1009.9		0		−1.83171				0		−1.41945	+	1.72776i		0			−	1.00000i		0		0.355171				0
1009.10		0		−1.83171				0		−1.41945	−	1.72776i		0				1.00000i		0		0.355171				0
1009.11		0		−1.65329				0		2.21195	+	0.327549i		0				1.00000i		0		−0.266637				0
1009.12		0		−1.65329				0		2.21195	−	0.327549i		0			−	1.00000i		0		−0.266637				0
1009.13		0		−0.460762				0		−2.19557	+	0.423658i		0				1.00000i		0		−2.78770				0
1009.14		0		−0.460762				0		−2.19557	−	0.423658i		0			−	1.00000i		0		−2.78770				0
1009.15		0		−0.359051				0		−0.565870	+	2.16328i		0				1.00000i		0		−2.87108				0
1009.16		0		−0.359051				0		−0.565870	−	2.16328i		0			−	1.00000i		0		−2.87108				0
1009.17		0		−0.319826				0		1.20181	+	1.88564i		0			−	1.00000i		0		−2.89771				0
1009.18		0		−0.319826				0		1.20181	−	1.88564i		0				1.00000i		0		−2.89771				0
1009.19		0		0.319826				0		−1.20181	+	1.88564i		0				1.00000i		0		−2.89771				0
1009.20		0		0.319826				0		−1.20181	−	1.88564i		0			−	1.00000i		0		−2.89771				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.b	even	2	1	inner
40.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1120.2.l.a		36
4.b	odd	2	1		280.2.l.a	✓	36
5.b	even	2	1	inner	1120.2.l.a		36
8.b	even	2	1	inner	1120.2.l.a		36
8.d	odd	2	1		280.2.l.a	✓	36
20.d	odd	2	1		280.2.l.a	✓	36
40.e	odd	2	1		280.2.l.a	✓	36
40.f	even	2	1	inner	1120.2.l.a		36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.2.l.a	✓	36	4.b	odd	2	1
280.2.l.a	✓	36	8.d	odd	2	1
280.2.l.a	✓	36	20.d	odd	2	1
280.2.l.a	✓	36	40.e	odd	2	1
1120.2.l.a		36	1.a	even	1	1	trivial
1120.2.l.a		36	5.b	even	2	1	inner
1120.2.l.a		36	8.b	even	2	1	inner
1120.2.l.a		36	40.f	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1120, [\chi])\).