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

• Label: 60.6.h
• Level: $60$
• Weight: $6$
• Character orbit: 60.h
• Rep. character: $\chi_{60}(59,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	64	64	0
Cusp forms	56	56	0
Eisenstein series	8	8	0

Trace form

\( 56 q - 14 q^{4} + 62 q^{6} - 4 q^{9} + O(q^{10}) \)

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.h.a	$60$	$6$	60.h	60.h	$2$	$4$	$4$	$9.623$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+4\beta _{1}q^{2}+(10\beta _{1}+\beta _{2})q^{3}-2^{5}q^{4}+\cdots\)
60.6.h.b	$60$	$6$	60.h	60.h	$2$	$4$	$4$	$9.623$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+9\beta _{1}q^{3}+(31-\beta _{3})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
60.6.h.c	$60$	$6$	60.h	60.h	$2$	$48$	$48$	$9.623$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$