Newform orbit 2268.2.bm.j

• Label: 2268.2.bm.j
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.bm
• 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.bm (of order \(6\), degree \(2\), not 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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
593.1		0			0			0		−4.23916				0		0.764306	−	2.53295i		0			0			0
593.2		0			0			0		−3.53988				0		0.163762	+	2.64068i		0			0			0
593.3		0			0			0		−2.86458				0		−2.00236	−	1.72932i		0			0			0
593.4		0			0			0		−2.00351				0		1.37922	−	2.25782i		0			0			0
593.5		0			0			0		−1.79338				0		−2.24756	−	1.39589i		0			0			0
593.6		0			0			0		−1.13332				0		−1.77285	+	1.96392i		0			0			0
593.7		0			0			0		−0.880270				0		2.07060	+	1.64700i		0			0			0
593.8		0			0			0		−0.0584093				0		2.64489	−	0.0676789i		0			0			0
593.9		0			0			0		0.0584093				0		2.64489	−	0.0676789i		0			0			0
593.10		0			0			0		0.880270				0		2.07060	+	1.64700i		0			0			0
593.11		0			0			0		1.13332				0		−1.77285	+	1.96392i		0			0			0
593.12		0			0			0		1.79338				0		−2.24756	−	1.39589i		0			0			0
593.13		0			0			0		2.00351				0		1.37922	−	2.25782i		0			0			0
593.14		0			0			0		2.86458				0		−2.00236	−	1.72932i		0			0			0
593.15		0			0			0		3.53988				0		0.163762	+	2.64068i		0			0			0
593.16		0			0			0		4.23916				0		0.764306	−	2.53295i		0			0			0
1025.1		0			0			0		−4.23916				0		0.764306	+	2.53295i		0			0			0
1025.2		0			0			0		−3.53988				0		0.163762	−	2.64068i		0			0			0
1025.3		0			0			0		−2.86458				0		−2.00236	+	1.72932i		0			0			0
1025.4		0			0			0		−2.00351				0		1.37922	+	2.25782i		0			0			0

Inner twists

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

    

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2268, [\chi])\):

\( T_{5}^{16} - 48T_{5}^{14} + 864T_{5}^{12} - 7416T_{5}^{10} + 32202T_{5}^{8} - 69876T_{5}^{6} + 68769T_{5}^{4} - 23976T_{5}^{2} + 81 \)

T13^16 + 6*T13^15 - 45*T13^14 - 342*T13^13 + 1845*T13^12 + 8928*T13^11 - 41292*T13^10 - 142074*T13^9 + 782937*T13^8 + 487728*T13^7 - 5516910*T13^6 - 700002*T13^5 + 29446416*T13^4 - 21291660*T13^3 - 39186342*T13^2 + 25050870*T13 + 50936769