Space of modular forms of level 60, weight 4, and Character 60.j

• Label: 60.4.j
• Level: $60$
• Weight: $4$
• Character orbit: 60.j
• Rep. character: $\chi_{60}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(60, [\chi])\).

	Total	New	Old
Modular forms	80	36	44
Cusp forms	64	36	28
Eisenstein series	16	0	16

Trace form

\( 36 q - 12 q^{6} + 84 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(60, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.4.j.a	$60$	$4$	60.j	20.e	$4$	$8$	$4$	$3.540$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{2}+\beta _{4})q^{2}+3\beta _{5}q^{3}+(6\beta _{3}+2\beta _{6}+\cdots)q^{4}+\cdots\)
60.4.j.b	$60$	$4$	60.j	20.e	$4$	$28$	$14$	$3.540$		None		$4$	$0$	\(0\)	\(0\)	\(24\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)