Newform orbit 5292.2.l.j

• Label: 5292.2.l.j
• Level: $5292$
• Weight: $2$
• Character orbit: 5292.l
• Analytic conductor: $42.257$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.l (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(42.2568327497\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	no (minimal twist has level 1764)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{11} - 16 q^{23} + 24 q^{25} + 32 q^{29} - 12 q^{37} + 16 q^{53} + 36 q^{65} + 12 q^{67} - 48 q^{71} + 12 q^{79} + 12 q^{85} - 32 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
361.1		0			0			0		−3.89246				0			0			0			0			0
361.2		0			0			0		−3.47961				0			0			0			0			0
361.3		0			0			0		−2.38486				0			0			0			0			0
361.4		0			0			0		−1.47387				0			0			0			0			0
361.5		0			0			0		−0.938454				0			0			0			0			0
361.6		0			0			0		−0.0223826				0			0			0			0			0
361.7		0			0			0		0.0223826				0			0			0			0			0
361.8		0			0			0		0.938454				0			0			0			0			0
361.9		0			0			0		1.47387				0			0			0			0			0
361.10		0			0			0		2.38486				0			0			0			0			0
361.11		0			0			0		3.47961				0			0			0			0			0
361.12		0			0			0		3.89246				0			0			0			0			0
3313.1		0			0			0		−3.89246				0			0			0			0			0
3313.2		0			0			0		−3.47961				0			0			0			0			0
3313.3		0			0			0		−2.38486				0			0			0			0			0
3313.4		0			0			0		−1.47387				0			0			0			0			0
3313.5		0			0			0		−0.938454				0			0			0			0			0
3313.6		0			0			0		−0.0223826				0			0			0			0			0
3313.7		0			0			0		0.0223826				0			0			0			0			0
3313.8		0			0			0		0.938454				0			0			0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
63.g	even	3	1	inner
63.k	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5292.2.l.j		24
3.b	odd	2	1		1764.2.l.j		24
7.b	odd	2	1	inner	5292.2.l.j		24
7.c	even	3	1		5292.2.i.j		24
7.c	even	3	1		5292.2.j.i		24
7.d	odd	6	1		5292.2.i.j		24
7.d	odd	6	1		5292.2.j.i		24
9.c	even	3	1		5292.2.i.j		24
9.d	odd	6	1		1764.2.i.j		24
21.c	even	2	1		1764.2.l.j		24
21.g	even	6	1		1764.2.i.j		24
21.g	even	6	1		1764.2.j.i	✓	24
21.h	odd	6	1		1764.2.i.j		24
21.h	odd	6	1		1764.2.j.i	✓	24
63.g	even	3	1	inner	5292.2.l.j		24
63.h	even	3	1		5292.2.j.i		24
63.i	even	6	1		1764.2.j.i	✓	24
63.j	odd	6	1		1764.2.j.i	✓	24
63.k	odd	6	1	inner	5292.2.l.j		24
63.l	odd	6	1		5292.2.i.j		24
63.n	odd	6	1		1764.2.l.j		24
63.o	even	6	1		1764.2.i.j		24
63.s	even	6	1		1764.2.l.j		24
63.t	odd	6	1		5292.2.j.i		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1764.2.i.j		24	9.d	odd	6	1
1764.2.i.j		24	21.g	even	6	1
1764.2.i.j		24	21.h	odd	6	1
1764.2.i.j		24	63.o	even	6	1
1764.2.j.i	✓	24	21.g	even	6	1
1764.2.j.i	✓	24	21.h	odd	6	1
1764.2.j.i	✓	24	63.i	even	6	1
1764.2.j.i	✓	24	63.j	odd	6	1
1764.2.l.j		24	3.b	odd	2	1
1764.2.l.j		24	21.c	even	2	1
1764.2.l.j		24	63.n	odd	6	1
1764.2.l.j		24	63.s	even	6	1
5292.2.i.j		24	7.c	even	3	1
5292.2.i.j		24	7.d	odd	6	1
5292.2.i.j		24	9.c	even	3	1
5292.2.i.j		24	63.l	odd	6	1
5292.2.j.i		24	7.c	even	3	1
5292.2.j.i		24	7.d	odd	6	1
5292.2.j.i		24	63.h	even	3	1
5292.2.j.i		24	63.t	odd	6	1
5292.2.l.j		24	1.a	even	1	1	trivial
5292.2.l.j		24	7.b	odd	2	1	inner
5292.2.l.j		24	63.g	even	3	1	inner
5292.2.l.j		24	63.k	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} - 36T_{5}^{10} + 441T_{5}^{8} - 2140T_{5}^{6} + 3834T_{5}^{4} - 1998T_{5}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(5292, [\chi])\).