Newform orbit 6048.2.c.g

• Label: 6048.2.c.g
• Level: $6048$
• Weight: $2$
• Character orbit: 6048.c
• Analytic conductor: $48.294$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(48.2935231425\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3025.1		0			0			0			−	3.66698i		0		−1.00000				0			0			0
3025.2		0			0			0			−	3.66698i		0		−1.00000				0			0			0
3025.3		0			0			0			−	3.11390i		0		−1.00000				0			0			0
3025.4		0			0			0			−	3.11390i		0		−1.00000				0			0			0
3025.5		0			0			0			−	2.52623i		0		−1.00000				0			0			0
3025.6		0			0			0			−	2.52623i		0		−1.00000				0			0			0
3025.7		0			0			0			−	1.58470i		0		−1.00000				0			0			0
3025.8		0			0			0			−	1.58470i		0		−1.00000				0			0			0
3025.9		0			0			0			−	1.53368i		0		−1.00000				0			0			0
3025.10		0			0			0			−	1.53368i		0		−1.00000				0			0			0
3025.11		0			0			0			−	1.26947i		0		−1.00000				0			0			0
3025.12		0			0			0			−	1.26947i		0		−1.00000				0			0			0
3025.13		0			0			0				1.26947i		0		−1.00000				0			0			0
3025.14		0			0			0				1.26947i		0		−1.00000				0			0			0
3025.15		0			0			0				1.53368i		0		−1.00000				0			0			0
3025.16		0			0			0				1.53368i		0		−1.00000				0			0			0
3025.17		0			0			0				1.58470i		0		−1.00000				0			0			0
3025.18		0			0			0				1.58470i		0		−1.00000				0			0			0
3025.19		0			0			0				2.52623i		0		−1.00000				0			0			0
3025.20		0			0			0				2.52623i		0		−1.00000				0			0			0

Inner twists

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

Twists

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

    

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(6048, [\chi])\):

\( T_{5}^{12} + 36T_{5}^{10} + 483T_{5}^{8} + 3048T_{5}^{6} + 9491T_{5}^{4} + 14084T_{5}^{2} + 7921 \)

\( T_{17}^{12} - 124T_{17}^{10} + 5788T_{17}^{8} - 128800T_{17}^{6} + 1407472T_{17}^{4} - 6700992T_{17}^{2} + 8156736 \)