Space of modular forms of level 60, weight 2, and Character 60.h

• Label: 60.2.h
• Level: $60$
• Weight: $2$
• Character orbit: 60.h
• Rep. character: $\chi_{60}(59,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(60, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

Trace form

8 * q - 6 * q^4 + 2 * q^6 - 4 * q^9 - 10 * q^10 + 2 * q^16 - 20 * q^21 + 26 * q^24 + 20 * q^30 + 20 * q^34 - 22 * q^36 + 10 * q^40 + 20 * q^45 - 4 * q^46 - 16 * q^49 - 46 * q^54 - 30 * q^60 + 24 * q^61 - 54 * q^64 + 28 * q^69 - 40 * q^70 + 60 * q^76 + 32 * q^81 + 40 * q^84 - 40 * q^85 + 30 * q^90 + 92 * q^94 - 22 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.2.h.a	$60$	$2$	60.h	60.h	$2$	$4$	$4$	$0.479$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		✓			60.2.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots\)
60.2.h.b	$60$	$2$	60.h	60.h	$2$	$4$	$4$	$0.479$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		✓			60.2.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)