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

• Label: 220.2.b
• Level: $220$
• Weight: $2$
• Character orbit: 220.b
• Rep. character: $\chi_{220}(89,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	42	6	36
Cusp forms	30	6	24
Eisenstein series	12	0	12

Trace form

\( 6 q - q^{5} - 4 q^{9} + O(q^{10}) \)

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.b.a	$220$	$2$	220.b	5.b	$2$	$2$	$2$	$1.757$	\(\Q(\sqrt{-1}) \)	None		✓			220.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{5}+iq^{7}+3q^{9}-q^{11}+\cdots\)
220.2.b.b	$220$	$2$	220.b	5.b	$2$	$4$	$4$	$1.757$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓	✓		220.2.b.b	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)