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

• Label: 60.4.h
• Level: $60$
• Weight: $4$
• Character orbit: 60.h
• Rep. character: $\chi_{60}(59,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(48\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	40	40	0
Cusp forms	32	32	0
Eisenstein series	8	8	0

Trace form

\( 32 q + 2 q^{4} + 14 q^{6} - 4 q^{9} + O(q^{10}) \)

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.h.a	$60$	$4$	60.h	60.h	$2$	$4$	$4$	$3.540$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}-4\beta _{2})q^{3}-8q^{4}-5\beta _{3}q^{5}+\cdots\)
60.4.h.b	$60$	$4$	60.h	60.h	$2$	$4$	$4$	$3.540$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
60.4.h.c	$60$	$4$	60.h	60.h	$2$	$24$	$24$	$3.540$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$