Newform orbit 2288.2.b.b

• Label: 2288.2.b.b
• Level: $2288$
• Weight: $2$
• Character orbit: 2288.b
• Analytic conductor: $18.270$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2288 = 2^{4} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2288.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.2697719825\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2287.1		0			−	2.87113i		0			−	1.50868i		0			−	3.04029i		0		−5.24338				0
2287.2		0			−	2.87113i		0			−	1.50868i		0				3.04029i		0		−5.24338				0
2287.3		0			−	2.87113i		0				1.50868i		0			−	3.04029i		0		−5.24338				0
2287.4		0			−	2.87113i		0				1.50868i		0				3.04029i		0		−5.24338				0
2287.5		0			−	1.60689i		0			−	1.80669i		0			−	1.89264i		0		0.417900				0
2287.6		0			−	1.60689i		0			−	1.80669i		0				1.89264i		0		0.417900				0
2287.7		0			−	1.60689i		0				1.80669i		0			−	1.89264i		0		0.417900				0
2287.8		0			−	1.60689i		0				1.80669i		0				1.89264i		0		0.417900				0
2287.9		0			−	1.08375i		0			−	3.66875i		0			−	1.47463i		0		1.82548				0
2287.10		0			−	1.08375i		0			−	3.66875i		0				1.47463i		0		1.82548				0
2287.11		0			−	1.08375i		0				3.66875i		0			−	1.47463i		0		1.82548				0
2287.12		0			−	1.08375i		0				3.66875i		0				1.47463i		0		1.82548				0
2287.13		0				1.08375i		0			−	3.66875i		0			−	1.47463i		0		1.82548				0
2287.14		0				1.08375i		0			−	3.66875i		0				1.47463i		0		1.82548				0
2287.15		0				1.08375i		0				3.66875i		0			−	1.47463i		0		1.82548				0
2287.16		0				1.08375i		0				3.66875i		0				1.47463i		0		1.82548				0
2287.17		0				1.60689i		0			−	1.80669i		0			−	1.89264i		0		0.417900				0
2287.18		0				1.60689i		0			−	1.80669i		0				1.89264i		0		0.417900				0
2287.19		0				1.60689i		0				1.80669i		0			−	1.89264i		0		0.417900				0
2287.20		0				1.60689i		0				1.80669i		0				1.89264i		0		0.417900				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
11.b	odd	2	1	inner
13.b	even	2	1	inner
44.c	even	2	1	inner
52.b	odd	2	1	inner
143.d	odd	2	1	inner
572.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2288.2.b.b	✓	24
4.b	odd	2	1	inner	2288.2.b.b	✓	24
11.b	odd	2	1	inner	2288.2.b.b	✓	24
13.b	even	2	1	inner	2288.2.b.b	✓	24
44.c	even	2	1	inner	2288.2.b.b	✓	24
52.b	odd	2	1	inner	2288.2.b.b	✓	24
143.d	odd	2	1	inner	2288.2.b.b	✓	24
572.b	even	2	1	inner	2288.2.b.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2288.2.b.b	✓	24	1.a	even	1	1	trivial
2288.2.b.b	✓	24	4.b	odd	2	1	inner
2288.2.b.b	✓	24	11.b	odd	2	1	inner
2288.2.b.b	✓	24	13.b	even	2	1	inner
2288.2.b.b	✓	24	44.c	even	2	1	inner
2288.2.b.b	✓	24	52.b	odd	2	1	inner
2288.2.b.b	✓	24	143.d	odd	2	1	inner
2288.2.b.b	✓	24	572.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{6} + 12T_{3}^{4} + 34T_{3}^{2} + 25 \) acting on \(S_{2}^{\mathrm{new}}(2288, [\chi])\).