Space of modular forms of level 220, weight 3, and Character 220.c

• Label: 220.3.c
• Level: $220$
• Weight: $3$
• Character orbit: 220.c
• Rep. character: $\chi_{220}(111,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.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 \(M_{3}(220, [\chi])\).

	Total	New	Old
Modular forms	76	40	36
Cusp forms	68	40	28
Eisenstein series	8	0	8

Trace form

40 * q - 4 * q^4 + 36 * q^8 - 120 * q^9 + 20 * q^10 - 80 * q^12 + 32 * q^13 - 56 * q^14 + 40 * q^16 + 16 * q^18 - 20 * q^20 - 80 * q^21 + 104 * q^24 + 200 * q^25 + 100 * q^26 + 60 * q^28 - 48 * q^29 - 280 * q^32 + 8 * q^34 + 160 * q^36 + 160 * q^37 - 200 * q^38 - 80 * q^40 - 120 * q^42 + 44 * q^44 + 80 * q^45 + 120 * q^46 - 16 * q^48 - 376 * q^49 - 36 * q^52 + 296 * q^54 - 40 * q^56 + 288 * q^57 + 96 * q^58 + 60 * q^60 - 160 * q^61 - 16 * q^62 + 500 * q^64 - 220 * q^66 + 116 * q^68 - 304 * q^69 - 60 * q^70 - 380 * q^72 - 480 * q^73 - 320 * q^74 - 480 * q^76 + 744 * q^78 - 80 * q^80 + 280 * q^81 - 480 * q^82 + 16 * q^84 + 320 * q^85 - 460 * q^86 + 224 * q^89 - 60 * q^90 + 24 * q^92 + 480 * q^93 + 432 * q^94 + 424 * q^96 + 720 * q^97 + 680 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(220, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.3.c.a	$220$	$3$	220.c	4.b	$2$	$40$	$40$	$5.995$		None		✓	✓	✓	220.3.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)