Space of modular forms of level 44, weight 9, and Character 44.h

• Label: 44.9.h
• Level: $44$
• Weight: $9$
• Character orbit: 44.h
• Rep. character: $\chi_{44}(3,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	44.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(44, [\chi])\).

	Total	New	Old
Modular forms	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

\( 184 q + 3 q^{2} + 183 q^{4} - 6 q^{5} - 515 q^{6} - 4233 q^{8} + 88040 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(44, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
44.9.h.a	$44$	$9$	44.h	44.h	$10$	$184$	$46$	$17.925$		None		✓	44.9.h.a	$4$	$0$	\(3\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$