Space of modular forms of level 44, weight 2, and Character 44.c

• Label: 44.2.c
• Level: $44$
• Weight: $2$
• Character orbit: 44.c
• Rep. character: $\chi_{44}(43,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	44.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(44, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

4 * q - 4 * q^4 - 4 * q^5 + 12 * q^12 - 8 * q^14 - 8 * q^16 + 4 * q^20 + 8 * q^22 - 16 * q^25 + 24 * q^26 + 12 * q^33 - 24 * q^34 + 12 * q^37 + 8 * q^38 - 24 * q^42 - 12 * q^44 - 24 * q^48 + 4 * q^49 - 8 * q^53 + 32 * q^56 - 12 * q^60 + 32 * q^64 + 24 * q^66 + 36 * q^69 + 8 * q^70 - 32 * q^77 - 24 * q^78 + 8 * q^80 - 36 * q^81 + 24 * q^82 - 16 * q^86 - 32 * q^88 - 4 * q^89 - 36 * q^92 - 12 * q^93 + 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(44, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
44.2.c.a	$44$	$2$	44.c	44.c	$2$	$4$	$4$	$0.351$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓	✓	44.2.c.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)