Newform orbit 1140.2.y.a

• Label: 1140.2.y.a
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.y
• Analytic conductor: $9.103$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.10294583043\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1		0		−0.707107	−	0.707107i		0		1.76413	−	1.37399i		0		2.45104	+	2.45104i		0				1.00000i		0
37.2		0		−0.707107	−	0.707107i		0		−1.74270	+	1.40107i		0		2.29396	+	2.29396i		0				1.00000i		0
37.3		0		−0.707107	−	0.707107i		0		−2.19115	−	0.445959i		0		−0.102192	−	0.102192i		0				1.00000i		0
37.4		0		−0.707107	−	0.707107i		0		−0.105511	+	2.23358i		0		−2.38118	−	2.38118i		0				1.00000i		0
37.5		0		−0.707107	−	0.707107i		0		0.260865	−	2.22080i		0		−0.450999	−	0.450999i		0				1.00000i		0
37.6		0		−0.707107	−	0.707107i		0		1.66093	+	1.49710i		0		−0.813205	−	0.813205i		0				1.00000i		0
37.7		0		−0.707107	−	0.707107i		0		0.175336	+	2.22918i		0		2.65404	+	2.65404i		0				1.00000i		0
37.8		0		−0.707107	−	0.707107i		0		2.23518	−	0.0631414i		0		−0.462950	−	0.462950i		0				1.00000i		0
37.9		0		−0.707107	−	0.707107i		0		−1.45042	−	1.70184i		0		1.40893	+	1.40893i		0				1.00000i		0
37.10		0		−0.707107	−	0.707107i		0		−1.60666	−	1.55520i		0		−3.59745	−	3.59745i		0				1.00000i		0
37.11		0		0.707107	+	0.707107i		0		−1.74270	+	1.40107i		0		2.29396	+	2.29396i		0				1.00000i		0
37.12		0		0.707107	+	0.707107i		0		−0.105511	+	2.23358i		0		−2.38118	−	2.38118i		0				1.00000i		0
37.13		0		0.707107	+	0.707107i		0		−2.19115	−	0.445959i		0		−0.102192	−	0.102192i		0				1.00000i		0
37.14		0		0.707107	+	0.707107i		0		1.66093	+	1.49710i		0		−0.813205	−	0.813205i		0				1.00000i		0
37.15		0		0.707107	+	0.707107i		0		1.76413	−	1.37399i		0		2.45104	+	2.45104i		0				1.00000i		0
37.16		0		0.707107	+	0.707107i		0		2.23518	−	0.0631414i		0		−0.462950	−	0.462950i		0				1.00000i		0
37.17		0		0.707107	+	0.707107i		0		0.260865	−	2.22080i		0		−0.450999	−	0.450999i		0				1.00000i		0
37.18		0		0.707107	+	0.707107i		0		−1.60666	−	1.55520i		0		−3.59745	−	3.59745i		0				1.00000i		0
37.19		0		0.707107	+	0.707107i		0		0.175336	+	2.22918i		0		2.65404	+	2.65404i		0				1.00000i		0
37.20		0		0.707107	+	0.707107i		0		−1.45042	−	1.70184i		0		1.40893	+	1.40893i		0				1.00000i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
19.b	odd	2	1	inner
95.g	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1140.2.y.a	✓	40
3.b	odd	2	1		3420.2.bb.f		40
5.c	odd	4	1	inner	1140.2.y.a	✓	40
15.e	even	4	1		3420.2.bb.f		40
19.b	odd	2	1	inner	1140.2.y.a	✓	40
57.d	even	2	1		3420.2.bb.f		40
95.g	even	4	1	inner	1140.2.y.a	✓	40
285.j	odd	4	1		3420.2.bb.f		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1140.2.y.a	✓	40	1.a	even	1	1	trivial
1140.2.y.a	✓	40	5.c	odd	4	1	inner
1140.2.y.a	✓	40	19.b	odd	2	1	inner
1140.2.y.a	✓	40	95.g	even	4	1	inner
3420.2.bb.f		40	3.b	odd	2	1
3420.2.bb.f		40	15.e	even	4	1
3420.2.bb.f		40	57.d	even	2	1
3420.2.bb.f		40	285.j	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1140, [\chi])\).