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

• Label: 220.3.h
• Level: $220$
• Weight: $3$
• Character orbit: 220.h
• Rep. character: $\chi_{220}(199,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• 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.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
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	60	16
Cusp forms	68	60	8
Eisenstein series	8	0	8

Trace form

60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

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.h.a	$220$	$3$	220.h	20.d	$2$	$60$	$60$	$5.995$		None		✓	✓	✓	220.3.h.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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