Space of modular forms of level 60, weight 5, and Character 60.f

• Label: 60.5.f
• Level: $60$
• Weight: $5$
• Character orbit: 60.f
• Rep. character: $\chi_{60}(19,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(60, [\chi])\).

	Total	New	Old
Modular forms	52	24	28
Cusp forms	44	24	20
Eisenstein series	8	0	8

Trace form

\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(60, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.5.f.a	$60$	$5$	60.f	20.d	$2$	$24$	$24$	$6.202$		None		$4$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)