Space of modular forms of level 60, weight 3, and Character 60.k

• Label: 60.3.k
• Level: $60$
• Weight: $3$
• Character orbit: 60.k
• Rep. character: $\chi_{60}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(60, [\chi])\).

	Total	New	Old
Modular forms	60	4	56
Cusp forms	36	4	32
Eisenstein series	24	0	24

Trace form

4 * q + 12 * q^5 + 20 * q^7 - 16 * q^11 - 24 * q^15 - 40 * q^17 - 24 * q^21 - 40 * q^23 - 16 * q^25 + 16 * q^31 + 60 * q^33 + 56 * q^35 + 200 * q^41 + 120 * q^43 - 12 * q^45 - 24 * q^51 - 200 * q^53 - 108 * q^55 + 120 * q^57 - 312 * q^61 + 60 * q^63 + 240 * q^65 - 40 * q^67 - 80 * q^71 - 20 * q^73 - 168 * q^75 - 200 * q^77 - 36 * q^81 - 240 * q^83 - 184 * q^85 + 60 * q^87 + 240 * q^91 + 120 * q^93 + 400 * q^95 + 300 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(60, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.3.k.a	$60$	$3$	60.k	5.c	$4$	$4$	$2$	$1.635$	\(\Q(i, \sqrt{6})\)	None		✓	✓	✓	60.3.k.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(60, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)