Space of modular forms of level 60, weight 9, and Character 60.c

• Label: 60.9.c
• Level: $60$
• Weight: $9$
• Character orbit: 60.c
• Rep. character: $\chi_{60}(31,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(60, [\chi])\).

	Total	New	Old
Modular forms	100	32	68
Cusp forms	92	32	60
Eisenstein series	8	0	8

Trace form

32 * q - 12 * q^2 - 134 * q^4 - 1134 * q^6 + 8460 * q^8 - 69984 * q^9 - 8750 * q^10 - 51392 * q^13 - 101604 * q^14 - 6782 * q^16 + 26244 * q^18 - 345000 * q^20 - 243648 * q^21 + 310196 * q^22 - 480654 * q^24 + 2500000 * q^25 - 1499604 * q^26 - 2638916 * q^28 - 4264704 * q^29 + 3377268 * q^32 - 1852604 * q^34 + 293058 * q^36 - 13729984 * q^37 - 6697320 * q^38 - 96250 * q^40 + 3397056 * q^41 + 1140156 * q^42 - 5284884 * q^44 + 11180552 * q^46 - 12365136 * q^48 - 5300960 * q^49 - 937500 * q^50 - 26421536 * q^52 - 4904064 * q^53 + 2480058 * q^54 + 28524948 * q^56 + 4650048 * q^57 - 18870492 * q^58 + 12048750 * q^60 - 8561600 * q^61 - 56320152 * q^62 - 6271262 * q^64 - 18120000 * q^65 + 73293660 * q^66 + 139566888 * q^68 + 8636544 * q^69 + 2632500 * q^70 - 18502020 * q^72 - 94303680 * q^73 - 28132428 * q^74 - 106287048 * q^76 + 267187584 * q^77 + 175264560 * q^78 + 58590000 * q^80 + 153055008 * q^81 + 162629800 * q^82 - 189340740 * q^84 + 106960000 * q^85 - 281163432 * q^86 - 271663540 * q^88 + 49084224 * q^89 + 19136250 * q^90 + 730860528 * q^92 + 34696512 * q^93 + 54603408 * q^94 - 138630366 * q^96 - 105865536 * q^97 - 382019580 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(60, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.9.c.a	$60$	$9$	60.c	4.b	$2$	$32$	$32$	$24.443$		None		✓	✓	✓	60.9.c.a	$2$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(60, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)