Space of modular forms of level 60, weight 12, and Character 60.h

• Label: 60.12.h
• Level: $60$
• Weight: $12$
• Character orbit: 60.h
• Rep. character: $\chi_{60}(59,\cdot)$
• Character field: $\Q$
• Dimension: $128$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(144\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(60, [\chi])\).

	Total	New	Old
Modular forms	136	136	0
Cusp forms	128	128	0
Eisenstein series	8	8	0

Trace form

\( 128 q - 1982 q^{4} + 4094 q^{6} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.12.h.a	$60$	$12$	60.h	60.h	$2$	$4$	$4$	$46.101$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		✓	60.12.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}\beta _{2}q^{2}+(23\beta _{1}-308\beta _{2})q^{3}-2^{11}q^{4}+\cdots\)
60.12.h.b	$60$	$12$	60.h	60.h	$2$	$4$	$4$	$46.101$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		✓	60.12.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-10\beta _{1}+33\beta _{2})q^{2}+(-3^{5}\beta _{1}+3^{5}\beta _{2}+\cdots)q^{3}+\cdots\)
60.12.h.c	$60$	$12$	60.h	60.h	$2$	$120$	$120$	$46.101$		None		✓	60.12.h.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$