Space of modular forms of level 220, weight 2, and Character 220.l

• Label: 220.2.l
• Level: $220$
• Weight: $2$
• Character orbit: 220.l
• Rep. character: $\chi_{220}(23,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $72$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(72\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(220, [\chi])\).

	Total	New	Old
Modular forms	80	60	20
Cusp forms	64	60	4
Eisenstein series	16	0	16

Trace form

60 * q - 8 * q^6 - 12 * q^8 - 4 * q^13 - 20 * q^17 + 28 * q^18 - 16 * q^21 - 20 * q^25 + 8 * q^26 - 20 * q^28 - 40 * q^30 - 40 * q^32 + 32 * q^36 + 20 * q^37 - 40 * q^38 + 40 * q^40 + 20 * q^45 + 40 * q^46 + 8 * q^48 + 4 * q^50 + 4 * q^52 - 20 * q^53 - 8 * q^56 - 32 * q^57 - 8 * q^58 - 80 * q^60 - 64 * q^61 - 36 * q^62 - 12 * q^65 + 52 * q^68 + 16 * q^70 - 20 * q^72 + 52 * q^73 + 8 * q^76 - 16 * q^80 + 20 * q^81 - 80 * q^82 - 20 * q^85 - 48 * q^86 + 24 * q^88 + 60 * q^90 + 56 * q^92 + 24 * q^93 + 16 * q^96 + 20 * q^97 - 64 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(220, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.2.l.a	$220$	$2$	220.l	20.e	$4$	$2$	$1$	$1.757$	\(\Q(\sqrt{-1}) \)	None		✓			220.2.l.a	$2$	$1$	\(-2\)	\(-4\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}+(-2 i-2)q^{3}-2 i q^{4}+\cdots\)
220.2.l.b	$220$	$2$	220.l	20.e	$4$	$2$	$1$	$1.757$	\(\Q(\sqrt{-1}) \)	None		✓			220.2.l.a	$2$	$0$	\(2\)	\(4\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}+(2 i+2)q^{3}-2 i q^{4}+\cdots\)
220.2.l.c	$220$	$2$	220.l	20.e	$4$	$28$	$14$	$1.757$		None		✓			220.2.l.c	$2$	$0$	\(-2\)	\(-4\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{4}]$
220.2.l.d	$220$	$2$	220.l	20.e	$4$	$28$	$14$	$1.757$		None		✓			220.2.l.c	$2$	$0$	\(2\)	\(4\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

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