Newform orbit 1764.2.bm.c

• Label: 1764.2.bm.c
• Level: $1764$
• Weight: $2$
• Character orbit: 1764.bm
• Analytic conductor: $14.086$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.0856109166\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1685.1		0		−1.67980	−	0.422207i		0		1.76434				0			0			0		2.64348	+	1.41845i		0
1685.2		0		−1.61111	+	0.635870i		0		−4.19356				0			0			0		2.19134	−	2.04891i		0
1685.3		0		−1.60072	−	0.661583i		0		−1.32437				0			0			0		2.12462	+	2.11802i		0
1685.4		0		−1.53224	+	0.807605i		0		1.49089				0			0			0		1.69555	−	2.47490i		0
1685.5		0		−1.34187	+	1.09516i		0		0.113102				0			0			0		0.601240	−	2.93913i		0
1685.6		0		−1.28699	−	1.15916i		0		−3.28666				0			0			0		0.312692	+	2.98366i		0
1685.7		0		−1.00057	−	1.41381i		0		2.62774				0			0			0		−0.997726	+	2.82923i		0
1685.8		0		−0.942894	+	1.45291i		0		1.64101				0			0			0		−1.22190	−	2.73988i		0
1685.9		0		−0.855097	−	1.50626i		0		−3.29237				0			0			0		−1.53762	+	2.57599i		0
1685.10		0		−0.602975	−	1.62371i		0		0.184109				0			0			0		−2.27284	+	1.95811i		0
1685.11		0		−0.371109	+	1.69183i		0		−2.14608				0			0			0		−2.72456	−	1.25571i		0
1685.12		0		−0.304737	−	1.70503i		0		3.38118				0			0			0		−2.81427	+	1.03917i		0
1685.13		0		0.304737	+	1.70503i		0		−3.38118				0			0			0		−2.81427	+	1.03917i		0
1685.14		0		0.371109	−	1.69183i		0		2.14608				0			0			0		−2.72456	−	1.25571i		0
1685.15		0		0.602975	+	1.62371i		0		−0.184109				0			0			0		−2.27284	+	1.95811i		0
1685.16		0		0.855097	+	1.50626i		0		3.29237				0			0			0		−1.53762	+	2.57599i		0
1685.17		0		0.942894	−	1.45291i		0		−1.64101				0			0			0		−1.22190	−	2.73988i		0
1685.18		0		1.00057	+	1.41381i		0		−2.62774				0			0			0		−0.997726	+	2.82923i		0
1685.19		0		1.28699	+	1.15916i		0		3.28666				0			0			0		0.312692	+	2.98366i		0
1685.20		0		1.34187	−	1.09516i		0		−0.113102				0			0			0		0.601240	−	2.93913i		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	1764.2.bm.c		48
3.b	odd	2	1		5292.2.bm.c		48
7.b	odd	2	1	inner	1764.2.bm.c		48
7.c	even	3	1		1764.2.w.c		48
7.c	even	3	1		1764.2.x.c	✓	48
7.d	odd	6	1		1764.2.w.c		48
7.d	odd	6	1		1764.2.x.c	✓	48
9.c	even	3	1		5292.2.w.c		48
9.d	odd	6	1		1764.2.w.c		48
21.c	even	2	1		5292.2.bm.c		48
21.g	even	6	1		5292.2.w.c		48
21.g	even	6	1		5292.2.x.c		48
21.h	odd	6	1		5292.2.w.c		48
21.h	odd	6	1		5292.2.x.c		48
63.g	even	3	1		5292.2.bm.c		48
63.h	even	3	1		5292.2.x.c		48
63.i	even	6	1		1764.2.x.c	✓	48
63.j	odd	6	1		1764.2.x.c	✓	48
63.k	odd	6	1		5292.2.bm.c		48
63.l	odd	6	1		5292.2.w.c		48
63.n	odd	6	1	inner	1764.2.bm.c		48
63.o	even	6	1		1764.2.w.c		48
63.s	even	6	1	inner	1764.2.bm.c		48
63.t	odd	6	1		5292.2.x.c		48

    

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

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