Newform orbit 1140.2.e.b

• Label: 1140.2.e.b
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.e
• Analytic conductor: $9.103$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.10294583043\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16 q^{9} + 24 q^{19} - 12 q^{25} + 24 q^{39} - 52 q^{45} + 16 q^{49} - 28 q^{55} + 8 q^{61} + 56 q^{81} - 28 q^{85} + 56 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
569.1		0		−1.65916	−	0.497190i		0		−0.826491	+	2.07772i		0				3.18676i		0		2.50560	+	1.64983i		0
569.2		0		−1.65916	−	0.497190i		0		0.826491	+	2.07772i		0			−	3.18676i		0		2.50560	+	1.64983i		0
569.3		0		−1.65916	+	0.497190i		0		−0.826491	−	2.07772i		0			−	3.18676i		0		2.50560	−	1.64983i		0
569.4		0		−1.65916	+	0.497190i		0		0.826491	−	2.07772i		0				3.18676i		0		2.50560	−	1.64983i		0
569.5		0		−0.800578	−	1.53593i		0		−2.20515	+	0.370556i		0			−	2.59637i		0		−1.71815	+	2.45926i		0
569.6		0		−0.800578	−	1.53593i		0		2.20515	+	0.370556i		0				2.59637i		0		−1.71815	+	2.45926i		0
569.7		0		−0.800578	+	1.53593i		0		−2.20515	−	0.370556i		0				2.59637i		0		−1.71815	−	2.45926i		0
569.8		0		−0.800578	+	1.53593i		0		2.20515	−	0.370556i		0			−	2.59637i		0		−1.71815	−	2.45926i		0
569.9		0		−0.325994	−	1.70110i		0		−1.09737	+	1.94827i		0			−	1.45033i		0		−2.78746	+	1.10909i		0
569.10		0		−0.325994	−	1.70110i		0		1.09737	+	1.94827i		0				1.45033i		0		−2.78746	+	1.10909i		0
569.11		0		−0.325994	+	1.70110i		0		−1.09737	−	1.94827i		0				1.45033i		0		−2.78746	−	1.10909i		0
569.12		0		−0.325994	+	1.70110i		0		1.09737	−	1.94827i		0			−	1.45033i		0		−2.78746	−	1.10909i		0
569.13		0		0.325994	−	1.70110i		0		−1.09737	−	1.94827i		0				1.45033i		0		−2.78746	−	1.10909i		0
569.14		0		0.325994	−	1.70110i		0		1.09737	−	1.94827i		0			−	1.45033i		0		−2.78746	−	1.10909i		0
569.15		0		0.325994	+	1.70110i		0		−1.09737	+	1.94827i		0			−	1.45033i		0		−2.78746	+	1.10909i		0
569.16		0		0.325994	+	1.70110i		0		1.09737	+	1.94827i		0				1.45033i		0		−2.78746	+	1.10909i		0
569.17		0		0.800578	−	1.53593i		0		−2.20515	−	0.370556i		0				2.59637i		0		−1.71815	−	2.45926i		0
569.18		0		0.800578	−	1.53593i		0		2.20515	−	0.370556i		0			−	2.59637i		0		−1.71815	−	2.45926i		0
569.19		0		0.800578	+	1.53593i		0		−2.20515	+	0.370556i		0			−	2.59637i		0		−1.71815	+	2.45926i		0
569.20		0		0.800578	+	1.53593i		0		2.20515	+	0.370556i		0				2.59637i		0		−1.71815	+	2.45926i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner
19.b	odd	2	1	inner
57.d	even	2	1	inner
95.d	odd	2	1	inner
285.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1140.2.e.b	✓	24
3.b	odd	2	1	inner	1140.2.e.b	✓	24
5.b	even	2	1	inner	1140.2.e.b	✓	24
15.d	odd	2	1	inner	1140.2.e.b	✓	24
19.b	odd	2	1	inner	1140.2.e.b	✓	24
57.d	even	2	1	inner	1140.2.e.b	✓	24
95.d	odd	2	1	inner	1140.2.e.b	✓	24
285.b	even	2	1	inner	1140.2.e.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1140.2.e.b	✓	24	1.a	even	1	1	trivial
1140.2.e.b	✓	24	3.b	odd	2	1	inner
1140.2.e.b	✓	24	5.b	even	2	1	inner
1140.2.e.b	✓	24	15.d	odd	2	1	inner
1140.2.e.b	✓	24	19.b	odd	2	1	inner
1140.2.e.b	✓	24	57.d	even	2	1	inner
1140.2.e.b	✓	24	95.d	odd	2	1	inner
1140.2.e.b	✓	24	285.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{6} + 19T_{7}^{4} + 104T_{7}^{2} + 144 \) acting on \(S_{2}^{\mathrm{new}}(1140, [\chi])\).