Newform orbit 567.2.p.e

• Label: 567.2.p.e
• Level: $567$
• Weight: $2$
• Character orbit: 567.p
• Analytic conductor: $4.528$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.52751779461\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{4} - 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
80.1	−2.28676	+	1.32026i		0		2.48619	−	4.30622i	−1.25340	−	2.17095i		0		−0.0580272	−	2.64511i			7.84868i		0		5.73246	+	3.30964i
80.2	−2.24330	+	1.29517i		0		2.35494	−	4.07887i	1.85700	+	3.21642i		0		−2.20314	+	1.46498i			7.01949i		0		−8.33163	−	4.81027i
80.3	−1.88023	+	1.08555i		0		1.35685	−	2.35014i	−0.618749	−	1.07170i		0		1.89307	+	1.84832i			1.54953i		0		2.32678	+	1.34337i
80.4	−1.41253	+	0.815523i		0		0.330156	−	0.571847i	−1.00291	−	1.73708i		0		−2.29841	+	1.31047i		−	2.18509i		0		2.83327	+	1.63579i
80.5	−0.972052	+	0.561215i		0		−0.370077	+	0.640991i	−0.115523	−	0.200091i		0		2.56041	−	0.666545i		−	3.07563i		0		0.224588	+	0.129666i
80.6	−0.886833	+	0.512013i		0		−0.475685	+	0.823911i	1.13548	+	1.96671i		0		−2.38431	−	1.14676i		−	3.02228i		0		−2.01397	−	1.16276i
80.7	−0.679931	+	0.392558i		0		−0.691796	+	1.19823i	0.893927	+	1.54833i		0		−0.596079	−	2.57773i		−	2.65651i		0		−1.21562	−	0.701837i
80.8	−0.118865	+	0.0686265i		0		−0.990581	+	1.71574i	−1.86818	−	3.23578i		0		1.08649	+	2.41237i		−	0.546426i		0		0.444120	+	0.256413i
80.9	0.118865	−	0.0686265i		0		−0.990581	+	1.71574i	1.86818	+	3.23578i		0		1.08649	+	2.41237i			0.546426i		0		0.444120	+	0.256413i
80.10	0.679931	−	0.392558i		0		−0.691796	+	1.19823i	−0.893927	−	1.54833i		0		−0.596079	−	2.57773i			2.65651i		0		−1.21562	−	0.701837i
80.11	0.886833	−	0.512013i		0		−0.475685	+	0.823911i	−1.13548	−	1.96671i		0		−2.38431	−	1.14676i			3.02228i		0		−2.01397	−	1.16276i
80.12	0.972052	−	0.561215i		0		−0.370077	+	0.640991i	0.115523	+	0.200091i		0		2.56041	−	0.666545i			3.07563i		0		0.224588	+	0.129666i
80.13	1.41253	−	0.815523i		0		0.330156	−	0.571847i	1.00291	+	1.73708i		0		−2.29841	+	1.31047i			2.18509i		0		2.83327	+	1.63579i
80.14	1.88023	−	1.08555i		0		1.35685	−	2.35014i	0.618749	+	1.07170i		0		1.89307	+	1.84832i		−	1.54953i		0		2.32678	+	1.34337i
80.15	2.24330	−	1.29517i		0		2.35494	−	4.07887i	−1.85700	−	3.21642i		0		−2.20314	+	1.46498i		−	7.01949i		0		−8.33163	−	4.81027i
80.16	2.28676	−	1.32026i		0		2.48619	−	4.30622i	1.25340	+	2.17095i		0		−0.0580272	−	2.64511i		−	7.84868i		0		5.73246	+	3.30964i
404.1	−2.28676	−	1.32026i		0		2.48619	+	4.30622i	−1.25340	+	2.17095i		0		−0.0580272	+	2.64511i		−	7.84868i		0		5.73246	−	3.30964i
404.2	−2.24330	−	1.29517i		0		2.35494	+	4.07887i	1.85700	−	3.21642i		0		−2.20314	−	1.46498i		−	7.01949i		0		−8.33163	+	4.81027i
404.3	−1.88023	−	1.08555i		0		1.35685	+	2.35014i	−0.618749	+	1.07170i		0		1.89307	−	1.84832i		−	1.54953i		0		2.32678	−	1.34337i
404.4	−1.41253	−	0.815523i		0		0.330156	+	0.571847i	−1.00291	+	1.73708i		0		−2.29841	−	1.31047i			2.18509i		0		2.83327	−	1.63579i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	567.2.p.e	✓	32
3.b	odd	2	1	inner	567.2.p.e	✓	32
7.d	odd	6	1	inner	567.2.p.e	✓	32
9.c	even	3	1		567.2.i.g		32
9.c	even	3	1		567.2.s.g		32
9.d	odd	6	1		567.2.i.g		32
9.d	odd	6	1		567.2.s.g		32
21.g	even	6	1	inner	567.2.p.e	✓	32
63.i	even	6	1		567.2.s.g		32
63.k	odd	6	1		567.2.i.g		32
63.s	even	6	1		567.2.i.g		32
63.t	odd	6	1		567.2.s.g		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
567.2.i.g		32	9.c	even	3	1
567.2.i.g		32	9.d	odd	6	1
567.2.i.g		32	63.k	odd	6	1
567.2.i.g		32	63.s	even	6	1
567.2.p.e	✓	32	1.a	even	1	1	trivial
567.2.p.e	✓	32	3.b	odd	2	1	inner
567.2.p.e	✓	32	7.d	odd	6	1	inner
567.2.p.e	✓	32	21.g	even	6	1	inner
567.2.s.g		32	9.c	even	3	1
567.2.s.g		32	9.d	odd	6	1
567.2.s.g		32	63.i	even	6	1
567.2.s.g		32	63.t	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 24*T2^30 + 351*T2^28 - 3304*T2^26 + 22899*T2^24 - 115560*T2^22 + 443850*T2^20 - 1257876*T2^18 + 2708559*T2^16 - 4256572*T2^14 + 5047818*T2^12 - 4281768*T2^10 + 2644306*T2^8 - 1019856*T2^6 + 247428*T2^4 - 4644*T2^2 + 81