Space of modular forms of level 48, weight 5, and Character 48.l

• Label: 48.5.l
• Level: $48$
• Weight: $5$
• Character orbit: 48.l
• Rep. character: $\chi_{48}(19,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(48, [\chi])\).

	Total	New	Old
Modular forms	68	32	36
Cusp forms	60	32	28
Eisenstein series	8	0	8

Trace form

\( 32 q + 12 q^{4} + 180 q^{8} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.5.l.a	$48$	$5$	48.l	16.f	$4$	$32$	$16$	$4.962$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)