Space of modular forms of level 44, weight 1, and Character 44.d

• Label: 44.1.d
• Level: $44$
• Weight: $1$
• Character orbit: 44.d
• Rep. character: $\chi_{44}(21,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	44.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(44, [\chi])\).

	Total	New	Old
Modular forms	4	1	3
Cusp forms	1	1	0
Eisenstein series	3	0	3

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^3 - q^5 + q^11 + q^15 - q^23 + q^27 - q^31 - q^33 - q^37 + 2 * q^47 + q^49 + 2 * q^53 - q^55 - q^59 - q^67 + q^69 - q^71 - q^81 - q^89 + q^93 - q^97

Decomposition of \(S_{1}^{\mathrm{new}}(44, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
44.1.d.a	$44$	$1$	44.d	11.b	$2$	$1$	$1$	$0.022$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None	✓	✓	✓	✓	44.1.d.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)