Newform orbit 2548.2.bq.g

• Label: 2548.2.bq.g
• Level: $2548$
• Weight: $2$
• Character orbit: 2548.bq
• Analytic conductor: $20.346$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.3458824350\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 20 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} - 40 q^{65} - 24 q^{71} + 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 20 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
361.1		0		−2.98281				0		−0.626773	+	0.361868i		0			0			0		5.89714				0
361.2		0		−2.62366				0		2.89137	−	1.66933i		0			0			0		3.88357				0
361.3		0		−1.87531				0		0.192850	−	0.111342i		0			0			0		0.516775				0
361.4		0		−1.22978				0		−2.34090	+	1.35152i		0			0			0		−1.48765				0
361.5		0		−0.901200				0		1.46259	−	0.844424i		0			0			0		−2.18784				0
361.6		0		−0.614820				0		−2.46799	+	1.42489i		0			0			0		−2.62200				0
361.7		0		0.614820				0		2.46799	−	1.42489i		0			0			0		−2.62200				0
361.8		0		0.901200				0		−1.46259	+	0.844424i		0			0			0		−2.18784				0
361.9		0		1.22978				0		2.34090	−	1.35152i		0			0			0		−1.48765				0
361.10		0		1.87531				0		−0.192850	+	0.111342i		0			0			0		0.516775				0
361.11		0		2.62366				0		−2.89137	+	1.66933i		0			0			0		3.88357				0
361.12		0		2.98281				0		0.626773	−	0.361868i		0			0			0		5.89714				0
1941.1		0		−2.98281				0		−0.626773	−	0.361868i		0			0			0		5.89714				0
1941.2		0		−2.62366				0		2.89137	+	1.66933i		0			0			0		3.88357				0
1941.3		0		−1.87531				0		0.192850	+	0.111342i		0			0			0		0.516775				0
1941.4		0		−1.22978				0		−2.34090	−	1.35152i		0			0			0		−1.48765				0
1941.5		0		−0.901200				0		1.46259	+	0.844424i		0			0			0		−2.18784				0
1941.6		0		−0.614820				0		−2.46799	−	1.42489i		0			0			0		−2.62200				0
1941.7		0		0.614820				0		2.46799	+	1.42489i		0			0			0		−2.62200				0
1941.8		0		0.901200				0		−1.46259	−	0.844424i		0			0			0		−2.18784				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
91.p	odd	6	1	inner
91.u	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2548.2.bq.g		24
7.b	odd	2	1	inner	2548.2.bq.g		24
7.c	even	3	1		2548.2.u.f	✓	24
7.c	even	3	1		2548.2.bb.g		24
7.d	odd	6	1		2548.2.u.f	✓	24
7.d	odd	6	1		2548.2.bb.g		24
13.e	even	6	1		2548.2.bb.g		24
91.k	even	6	1		2548.2.u.f	✓	24
91.l	odd	6	1		2548.2.u.f	✓	24
91.p	odd	6	1	inner	2548.2.bq.g		24
91.t	odd	6	1		2548.2.bb.g		24
91.u	even	6	1	inner	2548.2.bq.g		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2548.2.u.f	✓	24	7.c	even	3	1
2548.2.u.f	✓	24	7.d	odd	6	1
2548.2.u.f	✓	24	91.k	even	6	1
2548.2.u.f	✓	24	91.l	odd	6	1
2548.2.bb.g		24	7.c	even	3	1
2548.2.bb.g		24	7.d	odd	6	1
2548.2.bb.g		24	13.e	even	6	1
2548.2.bb.g		24	91.t	odd	6	1
2548.2.bq.g		24	1.a	even	1	1	trivial
2548.2.bq.g		24	7.b	odd	2	1	inner
2548.2.bq.g		24	91.p	odd	6	1	inner
2548.2.bq.g		24	91.u	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 22T_{3}^{10} + 171T_{3}^{8} - 572T_{3}^{6} + 837T_{3}^{4} - 508T_{3}^{2} + 100 \) acting on \(S_{2}^{\mathrm{new}}(2548, [\chi])\).