Newform orbit 5292.2.bm.c

• Label: 5292.2.bm.c
• Level: $5292$
• Weight: $2$
• Character orbit: 5292.bm
• Analytic conductor: $42.257$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.bm (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(42.2568327497\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 1764)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2285.1		0			0			0		−4.19356				0			0			0			0			0
2285.2		0			0			0		−3.38118				0			0			0			0			0
2285.3		0			0			0		−3.29237				0			0			0			0			0
2285.4		0			0			0		−3.28666				0			0			0			0			0
2285.5		0			0			0		−2.62774				0			0			0			0			0
2285.6		0			0			0		−2.14608				0			0			0			0			0
2285.7		0			0			0		−1.76434				0			0			0			0			0
2285.8		0			0			0		−1.64101				0			0			0			0			0
2285.9		0			0			0		−1.49089				0			0			0			0			0
2285.10		0			0			0		−1.32437				0			0			0			0			0
2285.11		0			0			0		−0.184109				0			0			0			0			0
2285.12		0			0			0		−0.113102				0			0			0			0			0
2285.13		0			0			0		0.113102				0			0			0			0			0
2285.14		0			0			0		0.184109				0			0			0			0			0
2285.15		0			0			0		1.32437				0			0			0			0			0
2285.16		0			0			0		1.49089				0			0			0			0			0
2285.17		0			0			0		1.64101				0			0			0			0			0
2285.18		0			0			0		1.76434				0			0			0			0			0
2285.19		0			0			0		2.14608				0			0			0			0			0
2285.20		0			0			0		2.62774				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.n	odd	6	1	inner
63.s	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5292.2.bm.c		48
3.b	odd	2	1		1764.2.bm.c		48
7.b	odd	2	1	inner	5292.2.bm.c		48
7.c	even	3	1		5292.2.w.c		48
7.c	even	3	1		5292.2.x.c		48
7.d	odd	6	1		5292.2.w.c		48
7.d	odd	6	1		5292.2.x.c		48
9.c	even	3	1		1764.2.w.c		48
9.d	odd	6	1		5292.2.w.c		48
21.c	even	2	1		1764.2.bm.c		48
21.g	even	6	1		1764.2.w.c		48
21.g	even	6	1		1764.2.x.c	✓	48
21.h	odd	6	1		1764.2.w.c		48
21.h	odd	6	1		1764.2.x.c	✓	48
63.g	even	3	1		1764.2.bm.c		48
63.h	even	3	1		1764.2.x.c	✓	48
63.i	even	6	1		5292.2.x.c		48
63.j	odd	6	1		5292.2.x.c		48
63.k	odd	6	1		1764.2.bm.c		48
63.l	odd	6	1		1764.2.w.c		48
63.n	odd	6	1	inner	5292.2.bm.c		48
63.o	even	6	1		5292.2.w.c		48
63.s	even	6	1	inner	5292.2.bm.c		48
63.t	odd	6	1		1764.2.x.c	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1764.2.w.c		48	9.c	even	3	1
1764.2.w.c		48	21.g	even	6	1
1764.2.w.c		48	21.h	odd	6	1
1764.2.w.c		48	63.l	odd	6	1
1764.2.x.c	✓	48	21.g	even	6	1
1764.2.x.c	✓	48	21.h	odd	6	1
1764.2.x.c	✓	48	63.h	even	3	1
1764.2.x.c	✓	48	63.t	odd	6	1
1764.2.bm.c		48	3.b	odd	2	1
1764.2.bm.c		48	21.c	even	2	1
1764.2.bm.c		48	63.g	even	3	1
1764.2.bm.c		48	63.k	odd	6	1
5292.2.w.c		48	7.c	even	3	1
5292.2.w.c		48	7.d	odd	6	1
5292.2.w.c		48	9.d	odd	6	1
5292.2.w.c		48	63.o	even	6	1
5292.2.x.c		48	7.c	even	3	1
5292.2.x.c		48	7.d	odd	6	1
5292.2.x.c		48	63.i	even	6	1
5292.2.x.c		48	63.j	odd	6	1
5292.2.bm.c		48	1.a	even	1	1	trivial
5292.2.bm.c		48	7.b	odd	2	1	inner
5292.2.bm.c		48	63.n	odd	6	1	inner
5292.2.bm.c		48	63.s	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 72*T5^22 + 2208*T5^20 - 37880*T5^18 + 401421*T5^16 - 2738940*T5^14 + 12173492*T5^12 - 34843572*T5^10 + 61712574*T5^8 - 61633528*T5^6 + 27239058*T5^4 - 1167828*T5^2 + 10609