Space of modular forms of level 55, weight 1, and Character 55.d

• Label: 55.1.d
• Level: $55$
• Weight: $1$
• Character orbit: 55.d
• Rep. character: $\chi_{55}(54,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	55.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(55, [\chi])\).

	Total	New	Old
Modular forms	3	3	0
Cusp forms	1	1	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.1.d.a	$55$	$1$	55.d	55.d	$2$	$1$	$1$	$0.027$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)