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

• Label: 60.2.d
• Level: $60$
• Weight: $2$
• Character orbit: 60.d
• Rep. character: $\chi_{60}(49,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	18	2	16
Cusp forms	6	2	4
Eisenstein series	12	0	12

Trace form

2 * q + 2 * q^5 - 2 * q^9 - 8 * q^11 - 4 * q^15 + 8 * q^21 - 6 * q^25 + 12 * q^29 + 8 * q^31 + 16 * q^35 - 20 * q^41 - 2 * q^45 - 18 * q^49 + 8 * q^51 - 8 * q^55 - 8 * q^59 + 4 * q^61 - 8 * q^69 - 8 * q^75 + 24 * q^79 + 2 * q^81 + 16 * q^85 + 20 * q^89 + 8 * q^99

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.d.a	$60$	$2$	60.d	5.b	$2$	$2$	$2$	$0.479$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	60.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(2 i+1)q^{5}-4 i q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(60, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)