Newform orbit 2288.2.b.c

• Label: 2288.2.b.c
• Level: $2288$
• Weight: $2$
• Character orbit: 2288.b
• Analytic conductor: $18.270$
• Analytic rank: $0$
• Dimension: $56$
• 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:	\(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 72 q^{9}+O(q^{10}) \)

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			−	3.16710i		0			−	3.14763i		0			−	2.40102i		0		−7.03050				0
2287.2		0			−	3.16710i		0			−	3.14763i		0				2.40102i		0		−7.03050				0
2287.3		0			−	3.16710i		0				3.14763i		0			−	2.40102i		0		−7.03050				0
2287.4		0			−	3.16710i		0				3.14763i		0				2.40102i		0		−7.03050				0
2287.5		0			−	2.96579i		0			−	1.16242i		0			−	2.18827i		0		−5.79592				0
2287.6		0			−	2.96579i		0			−	1.16242i		0				2.18827i		0		−5.79592				0
2287.7		0			−	2.96579i		0				1.16242i		0			−	2.18827i		0		−5.79592				0
2287.8		0			−	2.96579i		0				1.16242i		0				2.18827i		0		−5.79592				0
2287.9		0			−	2.08094i		0			−	4.28515i		0			−	3.10047i		0		−1.33031				0
2287.10		0			−	2.08094i		0			−	4.28515i		0				3.10047i		0		−1.33031				0
2287.11		0			−	2.08094i		0				4.28515i		0			−	3.10047i		0		−1.33031				0
2287.12		0			−	2.08094i		0				4.28515i		0				3.10047i		0		−1.33031				0
2287.13		0			−	2.05680i		0			−	1.33486i		0			−	2.15010i		0		−1.23043				0
2287.14		0			−	2.05680i		0			−	1.33486i		0				2.15010i		0		−1.23043				0
2287.15		0			−	2.05680i		0				1.33486i		0			−	2.15010i		0		−1.23043				0
2287.16		0			−	2.05680i		0				1.33486i		0				2.15010i		0		−1.23043				0
2287.17		0			−	1.16103i		0			−	1.21516i		0			−	0.788902i		0		1.65201				0
2287.18		0			−	1.16103i		0			−	1.21516i		0				0.788902i		0		1.65201				0
2287.19		0			−	1.16103i		0				1.21516i		0			−	0.788902i		0		1.65201				0
2287.20		0			−	1.16103i		0				1.21516i		0				0.788902i		0		1.65201				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.c	✓	56
4.b	odd	2	1	inner	2288.2.b.c	✓	56
11.b	odd	2	1	inner	2288.2.b.c	✓	56
13.b	even	2	1	inner	2288.2.b.c	✓	56
44.c	even	2	1	inner	2288.2.b.c	✓	56
52.b	odd	2	1	inner	2288.2.b.c	✓	56
143.d	odd	2	1	inner	2288.2.b.c	✓	56
572.b	even	2	1	inner	2288.2.b.c	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2288.2.b.c	✓	56	1.a	even	1	1	trivial
2288.2.b.c	✓	56	4.b	odd	2	1	inner
2288.2.b.c	✓	56	11.b	odd	2	1	inner
2288.2.b.c	✓	56	13.b	even	2	1	inner
2288.2.b.c	✓	56	44.c	even	2	1	inner
2288.2.b.c	✓	56	52.b	odd	2	1	inner
2288.2.b.c	✓	56	143.d	odd	2	1	inner
2288.2.b.c	✓	56	572.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} + 30T_{3}^{12} + 341T_{3}^{10} + 1847T_{3}^{8} + 4954T_{3}^{6} + 6131T_{3}^{4} + 2824T_{3}^{2} + 48 \) acting on \(S_{2}^{\mathrm{new}}(2288, [\chi])\).