Newform orbit 6048.2.j.c

• Label: 6048.2.j.c
• Level: $6048$
• Weight: $2$
• Character orbit: 6048.j
• Analytic conductor: $48.294$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6048.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(48.2935231425\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 1512)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5615.1		0			0			0		−3.61017				0				1.00000i		0			0			0
5615.2		0			0			0		−3.61017				0			−	1.00000i		0			0			0
5615.3		0			0			0		−3.47003				0				1.00000i		0			0			0
5615.4		0			0			0		−3.47003				0			−	1.00000i		0			0			0
5615.5		0			0			0		−2.21305				0				1.00000i		0			0			0
5615.6		0			0			0		−2.21305				0			−	1.00000i		0			0			0
5615.7		0			0			0		−2.09311				0				1.00000i		0			0			0
5615.8		0			0			0		−2.09311				0			−	1.00000i		0			0			0
5615.9		0			0			0		−1.17792				0			−	1.00000i		0			0			0
5615.10		0			0			0		−1.17792				0				1.00000i		0			0			0
5615.11		0			0			0		−0.436221				0				1.00000i		0			0			0
5615.12		0			0			0		−0.436221				0			−	1.00000i		0			0			0
5615.13		0			0			0		−0.206991				0				1.00000i		0			0			0
5615.14		0			0			0		−0.206991				0			−	1.00000i		0			0			0
5615.15		0			0			0		−0.162025				0				1.00000i		0			0			0
5615.16		0			0			0		−0.162025				0			−	1.00000i		0			0			0
5615.17		0			0			0		0.162025				0			−	1.00000i		0			0			0
5615.18		0			0			0		0.162025				0				1.00000i		0			0			0
5615.19		0			0			0		0.206991				0			−	1.00000i		0			0			0
5615.20		0			0			0		0.206991				0				1.00000i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.d	odd	2	1	inner
24.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	6048.2.j.c		32
3.b	odd	2	1	inner	6048.2.j.c		32
4.b	odd	2	1		1512.2.j.c	✓	32
8.b	even	2	1		1512.2.j.c	✓	32
8.d	odd	2	1	inner	6048.2.j.c		32
12.b	even	2	1		1512.2.j.c	✓	32
24.f	even	2	1	inner	6048.2.j.c		32
24.h	odd	2	1		1512.2.j.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1512.2.j.c	✓	32	4.b	odd	2	1
1512.2.j.c	✓	32	8.b	even	2	1
1512.2.j.c	✓	32	12.b	even	2	1
1512.2.j.c	✓	32	24.h	odd	2	1
6048.2.j.c		32	1.a	even	1	1	trivial
6048.2.j.c		32	3.b	odd	2	1	inner
6048.2.j.c		32	8.d	odd	2	1	inner
6048.2.j.c		32	24.f	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{16} - 36T_{5}^{14} + 468T_{5}^{12} - 2684T_{5}^{10} + 6806T_{5}^{8} - 6300T_{5}^{6} + 1300T_{5}^{4} - 68T_{5}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(6048, [\chi])\).