Space of modular forms of level 220, weight 1, and Character 220.e

• Label: 220.1.e
• Level: $220$
• Weight: $1$
• Character orbit: 220.e
• Rep. character: $\chi_{220}(109,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	220.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(220, [\chi])\).

	Total	New	Old
Modular forms	11	2	9
Cusp forms	5	2	3
Eisenstein series	6	0	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + q^{5} - 4 q^{9} - 2 q^{11} + 3 q^{15} - q^{25} + 2 q^{31} - 2 q^{45} - 2 q^{49} - q^{55} - 2 q^{59} + 6 q^{69} - 2 q^{71} + 3 q^{75} + 2 q^{81} + 2 q^{89} + 4 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(220, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.1.e.a	$220$	$1$	220.e	55.d	$2$	$2$	$2$	$0.110$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		✓	✓	✓	220.1.e.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)