Newform orbit 2268.2.t.c

• Label: 2268.2.t.c
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.t
• Analytic conductor: $18.110$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.1100711784\)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1781.1		0			0			0		−2.11958	−	3.67122i		0		−2.57575	−	0.604567i		0			0			0
1781.2		0			0			0		−1.76994	−	3.06563i		0		2.20501	+	1.46216i		0			0			0
1781.3		0			0			0		−1.43229	−	2.48080i		0		−0.496452	−	2.59876i		0			0			0
1781.4		0			0			0		−1.00175	−	1.73509i		0		−2.64494	+	0.0655283i		0			0			0
1781.5		0			0			0		−0.896692	−	1.55312i		0		−0.0850948	−	2.64438i		0			0			0
1781.6		0			0			0		−0.566658	−	0.981481i		0		2.58723	−	0.553375i		0			0			0
1781.7		0			0			0		−0.440135	−	0.762336i		0		0.391046	+	2.61669i		0			0			0
1781.8		0			0			0		−0.0292047	−	0.0505839i		0		−1.38105	+	2.25670i		0			0			0
1781.9		0			0			0		0.0292047	+	0.0505839i		0		−1.38105	+	2.25670i		0			0			0
1781.10		0			0			0		0.440135	+	0.762336i		0		0.391046	+	2.61669i		0			0			0
1781.11		0			0			0		0.566658	+	0.981481i		0		2.58723	−	0.553375i		0			0			0
1781.12		0			0			0		0.896692	+	1.55312i		0		−0.0850948	−	2.64438i		0			0			0
1781.13		0			0			0		1.00175	+	1.73509i		0		−2.64494	+	0.0655283i		0			0			0
1781.14		0			0			0		1.43229	+	2.48080i		0		−0.496452	−	2.59876i		0			0			0
1781.15		0			0			0		1.76994	+	3.06563i		0		2.20501	+	1.46216i		0			0			0
1781.16		0			0			0		2.11958	+	3.67122i		0		−2.57575	−	0.604567i		0			0			0
2105.1		0			0			0		−2.11958	+	3.67122i		0		−2.57575	+	0.604567i		0			0			0
2105.2		0			0			0		−1.76994	+	3.06563i		0		2.20501	−	1.46216i		0			0			0
2105.3		0			0			0		−1.43229	+	2.48080i		0		−0.496452	+	2.59876i		0			0			0
2105.4		0			0			0		−1.00175	+	1.73509i		0		−2.64494	−	0.0655283i		0			0			0

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	2268.2.t.c	✓	32
3.b	odd	2	1	inner	2268.2.t.c	✓	32
7.d	odd	6	1	inner	2268.2.t.c	✓	32
9.c	even	3	1		2268.2.w.j		32
9.c	even	3	1		2268.2.bm.j		32
9.d	odd	6	1		2268.2.w.j		32
9.d	odd	6	1		2268.2.bm.j		32
21.g	even	6	1	inner	2268.2.t.c	✓	32
63.i	even	6	1		2268.2.bm.j		32
63.k	odd	6	1		2268.2.w.j		32
63.s	even	6	1		2268.2.w.j		32
63.t	odd	6	1		2268.2.bm.j		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2268.2.t.c	✓	32	1.a	even	1	1	trivial
2268.2.t.c	✓	32	3.b	odd	2	1	inner
2268.2.t.c	✓	32	7.d	odd	6	1	inner
2268.2.t.c	✓	32	21.g	even	6	1	inner
2268.2.w.j		32	9.c	even	3	1
2268.2.w.j		32	9.d	odd	6	1
2268.2.w.j		32	63.k	odd	6	1
2268.2.w.j		32	63.s	even	6	1
2268.2.bm.j		32	9.c	even	3	1
2268.2.bm.j		32	9.d	odd	6	1
2268.2.bm.j		32	63.i	even	6	1
2268.2.bm.j		32	63.t	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^32 + 48*T5^30 + 1440*T5^28 + 26640*T5^26 + 358326*T5^24 + 3385908*T5^22 + 23958018*T5^20 + 121389192*T5^18 + 461653587*T5^16 + 1250884296*T5^14 + 2490489990*T5^12 + 3261753036*T5^10 + 3051220023*T5^8 + 1637485632*T5^6 + 569278287*T5^4 + 1942056*T5^2 + 6561