Space of modular forms of level 60, weight 7, and Character 60.k

• Label: 60.7.k
• Level: $60$
• Weight: $7$
• Character orbit: 60.k
• Rep. character: $\chi_{60}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(60, [\chi])\).

	Total	New	Old
Modular forms	156	12	144
Cusp forms	132	12	120
Eisenstein series	24	0	24

Trace form

\( 12 q + 312 q^{5} + 120 q^{7} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(60, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.7.k.a	$60$	$7$	60.k	5.c	$4$	$12$	$6$	$13.803$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(312\)	\(120\)	$2^{19}\cdot 3^{10}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+(26-4\beta _{1}+\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)