Newform orbit 576.3.n.c

• Label: 576.3.n.c
• Level: $576$
• Weight: $3$
• Character orbit: 576.n
• Analytic conductor: $15.695$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.6948632272\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 18 q^{5} + 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
353.1		0		−2.90962	−	0.730846i		0		3.09427	+	5.35943i		0		0.183090	−	0.317122i		0		7.93173	+	4.25296i		0
353.2		0		−2.81879	+	1.02686i		0		−1.79985	−	3.11744i		0		3.70215	−	6.41232i		0		6.89112	−	5.78899i		0
353.3		0		−2.77167	−	1.14797i		0		1.13094	+	1.95884i		0		2.43128	−	4.21109i		0		6.36431	+	6.36361i		0
353.4		0		−2.72431	+	1.25624i		0		−4.89158	−	8.47246i		0		−3.88386	+	6.72705i		0		5.84373	−	6.84477i		0
353.5		0		−1.32664	−	2.69073i		0		−2.27609	−	3.94230i		0		−4.81066	+	8.33232i		0		−5.48007	+	7.13924i		0
353.6		0		−1.21852	+	2.74139i		0		2.39677	+	4.15133i		0		−1.12793	+	1.95364i		0		−6.03041	−	6.68088i		0
353.7		0		−1.08485	+	2.79698i		0		−3.07518	−	5.32637i		0		−5.35886	+	9.28182i		0		−6.64619	−	6.06862i		0
353.8		0		−0.559363	−	2.94739i		0		0.920717	+	1.59473i		0		−4.56979	+	7.91511i		0		−8.37423	+	3.29733i		0
353.9		0		0.559363	+	2.94739i		0		0.920717	+	1.59473i		0		4.56979	−	7.91511i		0		−8.37423	+	3.29733i		0
353.10		0		1.08485	−	2.79698i		0		−3.07518	−	5.32637i		0		5.35886	−	9.28182i		0		−6.64619	−	6.06862i		0
353.11		0		1.21852	−	2.74139i		0		2.39677	+	4.15133i		0		1.12793	−	1.95364i		0		−6.03041	−	6.68088i		0
353.12		0		1.32664	+	2.69073i		0		−2.27609	−	3.94230i		0		4.81066	−	8.33232i		0		−5.48007	+	7.13924i		0
353.13		0		2.72431	−	1.25624i		0		−4.89158	−	8.47246i		0		3.88386	−	6.72705i		0		5.84373	−	6.84477i		0
353.14		0		2.77167	+	1.14797i		0		1.13094	+	1.95884i		0		−2.43128	+	4.21109i		0		6.36431	+	6.36361i		0
353.15		0		2.81879	−	1.02686i		0		−1.79985	−	3.11744i		0		−3.70215	+	6.41232i		0		6.89112	−	5.78899i		0
353.16		0		2.90962	+	0.730846i		0		3.09427	+	5.35943i		0		−0.183090	+	0.317122i		0		7.93173	+	4.25296i		0
545.1		0		−2.90962	+	0.730846i		0		3.09427	−	5.35943i		0		0.183090	+	0.317122i		0		7.93173	−	4.25296i		0
545.2		0		−2.81879	−	1.02686i		0		−1.79985	+	3.11744i		0		3.70215	+	6.41232i		0		6.89112	+	5.78899i		0
545.3		0		−2.77167	+	1.14797i		0		1.13094	−	1.95884i		0		2.43128	+	4.21109i		0		6.36431	−	6.36361i		0
545.4		0		−2.72431	−	1.25624i		0		−4.89158	+	8.47246i		0		−3.88386	−	6.72705i		0		5.84373	+	6.84477i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
72.j	odd	6	1	inner
72.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	576.3.n.c	✓	32
3.b	odd	2	1		1728.3.n.d		32
4.b	odd	2	1	inner	576.3.n.c	✓	32
8.b	even	2	1		576.3.n.d	yes	32
8.d	odd	2	1		576.3.n.d	yes	32
9.c	even	3	1		1728.3.n.c		32
9.d	odd	6	1		576.3.n.d	yes	32
12.b	even	2	1		1728.3.n.d		32
24.f	even	2	1		1728.3.n.c		32
24.h	odd	2	1		1728.3.n.c		32
36.f	odd	6	1		1728.3.n.c		32
36.h	even	6	1		576.3.n.d	yes	32
72.j	odd	6	1	inner	576.3.n.c	✓	32
72.l	even	6	1	inner	576.3.n.c	✓	32
72.n	even	6	1		1728.3.n.d		32
72.p	odd	6	1		1728.3.n.d		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
576.3.n.c	✓	32	1.a	even	1	1	trivial
576.3.n.c	✓	32	4.b	odd	2	1	inner
576.3.n.c	✓	32	72.j	odd	6	1	inner
576.3.n.c	✓	32	72.l	even	6	1	inner
576.3.n.d	yes	32	8.b	even	2	1
576.3.n.d	yes	32	8.d	odd	2	1
576.3.n.d	yes	32	9.d	odd	6	1
576.3.n.d	yes	32	36.h	even	6	1
1728.3.n.c		32	9.c	even	3	1
1728.3.n.c		32	24.f	even	2	1
1728.3.n.c		32	24.h	odd	2	1
1728.3.n.c		32	36.f	odd	6	1
1728.3.n.d		32	3.b	odd	2	1
1728.3.n.d		32	12.b	even	2	1
1728.3.n.d		32	72.n	even	6	1
1728.3.n.d		32	72.p	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^16 + 9*T5^15 + 159*T5^14 + 558*T5^13 + 9729*T5^12 + 25515*T5^11 + 394281*T5^10 + 449550*T5^9 + 8997399*T5^8 + 4261977*T5^7 + 145665621*T5^6 - 73614420*T5^5 + 1189433484*T5^4 - 1493913456*T5^3 + 7970162832*T5^2 - 8802027648*T5 + 14841086976