Space of modular forms of level 60, weight 6, and Character 60.i

• Label: 60.6.i
• Level: $60$
• Weight: $6$
• Character orbit: 60.i
• Rep. character: $\chi_{60}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(60, [\chi])\).

	Total	New	Old
Modular forms	132	20	112
Cusp forms	108	20	88
Eisenstein series	24	0	24

Trace form

\( 20 q + 2 q^{3} + 76 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(60, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.6.i.a	$60$	$6$	60.i	15.e	$4$	$20$	$10$	$9.623$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(76\)	$2^{23}\cdot 3^{14}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{3}-\beta _{5}q^{5}+(4+4\beta _{1}+\beta _{8})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)