Space of modular forms of level 6048, weight 2, and Character 6048.j

• Label: 6048.2.j
• Level: $6048$
• Weight: $2$
• Character orbit: 6048.j
• Rep. character: $\chi_{6048}(5615,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $2304$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6048.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2304\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6048, [\chi])\).

	Total	New	Old
Modular forms	1200	96	1104
Cusp forms	1104	96	1008
Eisenstein series	96	0	96

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6048, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6048.2.j.a	$6048$	$2$	6048.j	24.f	$2$	$8$	$8$	$48.294$	8.0.56070144.2	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{4})q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{6}+\cdots)q^{11}+\cdots\)
6048.2.j.b	$6048$	$2$	6048.j	24.f	$2$	$8$	$8$	$48.294$	8.0.56070144.2	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{4})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{6})q^{11}+\cdots\)
6048.2.j.c	$6048$	$2$	6048.j	24.f	$2$	$32$	$32$	$48.294$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
6048.2.j.d	$6048$	$2$	6048.j	24.f	$2$	$48$	$48$	$48.294$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(6048, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6048, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)