Space of modular forms of level 44, weight 4, and Character 44.c

• Label: 44.4.c
• Level: $44$
• Weight: $4$
• Character orbit: 44.c
• Rep. character: $\chi_{44}(43,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(44, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

16 * q - 12 * q^4 - 4 * q^5 - 132 * q^9 + 28 * q^12 + 104 * q^14 + 248 * q^16 - 300 * q^20 + 112 * q^22 + 364 * q^25 - 360 * q^26 - 116 * q^33 - 104 * q^34 - 184 * q^36 - 20 * q^37 - 696 * q^38 + 1176 * q^42 - 84 * q^44 - 888 * q^45 + 1192 * q^48 + 496 * q^49 + 1344 * q^53 - 2304 * q^56 + 1008 * q^58 + 1332 * q^60 - 960 * q^64 - 2536 * q^66 - 564 * q^69 - 2504 * q^70 - 1184 * q^77 + 5240 * q^78 + 744 * q^80 - 1656 * q^81 + 136 * q^82 + 1472 * q^86 + 3808 * q^88 + 252 * q^89 + 5100 * q^92 + 2140 * q^93 - 4004 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(44, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
44.4.c.a	$44$	$4$	44.c	44.c	$2$	$16$	$16$	$2.596$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	44.4.c.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{22}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)