Newform orbit 567.2.i.g

• Label: 567.2.i.g
• Level: $567$
• Weight: $2$
• Character orbit: 567.i
• Analytic conductor: $4.528$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.i (of order \(6\), degree \(2\), not 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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
215.1		−	2.64053i		0		−4.97239			1.25340	+	2.17095i		0		2.31975	−	1.27230i			7.84868i		0		5.73246	−	3.30964i
215.2		−	2.59034i		0		−4.70987			−1.85700	−	3.21642i		0		−0.167138	+	2.64047i			7.01949i		0		−8.33163	+	4.81027i
215.3		−	2.17111i		0		−2.71370			0.618749	+	1.07170i		0		−2.54723	−	0.715283i			1.54953i		0		2.32678	−	1.34337i
215.4		−	1.63105i		0		−0.660313			1.00291	+	1.73708i		0		0.0143018	+	2.64571i		−	2.18509i		0		2.83327	−	1.63579i
215.5		−	1.12243i		0		0.740153			0.115523	+	0.200091i		0		−0.702962	−	2.55066i		−	3.07563i		0		0.224588	−	0.129666i
215.6		−	1.02403i		0		0.951370			−1.13548	−	1.96671i		0		2.18528	+	1.49150i		−	3.02228i		0		−2.01397	+	1.16276i
215.7		−	0.785117i		0		1.38359			−0.893927	−	1.54833i		0		2.53042	−	0.772645i		−	2.65651i		0		−1.21562	+	0.701837i
215.8		−	0.137253i		0		1.98116			1.86818	+	3.23578i		0		−2.63242	+	0.265262i		−	0.546426i		0		0.444120	−	0.256413i
215.9			0.137253i		0		1.98116			−1.86818	−	3.23578i		0		−2.63242	+	0.265262i			0.546426i		0		0.444120	−	0.256413i
215.10			0.785117i		0		1.38359			0.893927	+	1.54833i		0		2.53042	−	0.772645i			2.65651i		0		−1.21562	+	0.701837i
215.11			1.02403i		0		0.951370			1.13548	+	1.96671i		0		2.18528	+	1.49150i			3.02228i		0		−2.01397	+	1.16276i
215.12			1.12243i		0		0.740153			−0.115523	−	0.200091i		0		−0.702962	−	2.55066i			3.07563i		0		0.224588	−	0.129666i
215.13			1.63105i		0		−0.660313			−1.00291	−	1.73708i		0		0.0143018	+	2.64571i			2.18509i		0		2.83327	−	1.63579i
215.14			2.17111i		0		−2.71370			−0.618749	−	1.07170i		0		−2.54723	−	0.715283i		−	1.54953i		0		2.32678	−	1.34337i
215.15			2.59034i		0		−4.70987			1.85700	+	3.21642i		0		−0.167138	+	2.64047i		−	7.01949i		0		−8.33163	+	4.81027i
215.16			2.64053i		0		−4.97239			−1.25340	−	2.17095i		0		2.31975	−	1.27230i		−	7.84868i		0		5.73246	−	3.30964i
269.1		−	2.64053i		0		−4.97239			−1.25340	+	2.17095i		0		2.31975	+	1.27230i			7.84868i		0		5.73246	+	3.30964i
269.2		−	2.59034i		0		−4.70987			1.85700	−	3.21642i		0		−0.167138	−	2.64047i			7.01949i		0		−8.33163	−	4.81027i
269.3		−	2.17111i		0		−2.71370			−0.618749	+	1.07170i		0		−2.54723	+	0.715283i			1.54953i		0		2.32678	+	1.34337i
269.4		−	1.63105i		0		−0.660313			−1.00291	+	1.73708i		0		0.0143018	−	2.64571i		−	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
63.i	even	6	1	inner
63.t	odd	6	1	inner

Twists

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

    

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(567, [\chi])\):

\( T_{2}^{16} + 24T_{2}^{14} + 225T_{2}^{12} + 1048T_{2}^{10} + 2574T_{2}^{8} + 3312T_{2}^{6} + 2092T_{2}^{4} + 516T_{2}^{2} + 9 \)

T11^32 - 84*T11^30 + 4431*T11^28 - 143116*T11^26 + 3349695*T11^24 - 53832312*T11^22 + 643805646*T11^20 - 5547727656*T11^18 + 35980998291*T11^16 - 167552112964*T11^14 + 575204566962*T11^12 - 1326161383428*T11^10 + 2240652678574*T11^8 - 2563754877624*T11^6 + 2113429675968*T11^4 - 1031380298856*T11^2 + 321499206081

T13^16 - 6*T13^15 - 45*T13^14 + 342*T13^13 + 1749*T13^12 - 17784*T13^11 + 4788*T13^10 + 310770*T13^9 - 465471*T13^8 - 4857624*T13^7 + 24832386*T13^6 - 50300190*T13^5 + 47154960*T13^4 - 15527700*T13^3 + 2485890*T13^2 - 196830*T13 + 6561