Space of modular forms of level 44, weight 3, and Character 44.h

• Label: 44.3.h
• Level: $44$
• Weight: $3$
• Character orbit: 44.h
• Rep. character: $\chi_{44}(3,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
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:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(44, [\chi])\).

	Total	New	Old
Modular forms	56	56	0
Cusp forms	40	40	0
Eisenstein series	16	16	0

Trace form

\( 40 q - 5 q^{2} - 9 q^{4} - 6 q^{5} - 11 q^{6} + 7 q^{8} + 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(44, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
44.3.h.a	$44$	$3$	44.h	44.h	$10$	$40$	$10$	$1.199$		None		✓	✓	✓	44.3.h.a	$4$	$0$	\(-5\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$