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

• Label: 44.3.b
• Level: $44$
• Weight: $3$
• Character orbit: 44.b
• Rep. character: $\chi_{44}(23,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
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	14	10	4
Cusp forms	10	10	0
Eisenstein series	4	0	4

Trace form

10 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 - 12 * q^8 - 30 * q^9 - 2 * q^10 + 40 * q^12 - 4 * q^13 - 4 * q^14 - 40 * q^16 + 20 * q^17 - 22 * q^18 - 64 * q^20 + 32 * q^21 + 36 * q^24 - 10 * q^25 - 36 * q^26 + 40 * q^28 + 28 * q^29 + 126 * q^30 + 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 - 12 * q^40 + 100 * q^41 + 260 * q^42 - 44 * q^44 - 44 * q^45 - 130 * q^46 + 24 * q^48 - 22 * q^49 - 198 * q^50 - 176 * q^52 + 100 * q^53 - 350 * q^54 + 136 * q^56 - 112 * q^57 + 116 * q^58 - 136 * q^60 - 52 * q^61 + 134 * q^62 - 368 * q^64 - 184 * q^65 + 110 * q^66 + 176 * q^68 + 184 * q^69 - 36 * q^70 + 360 * q^72 + 84 * q^73 + 362 * q^74 + 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 - 40 * q^84 - 216 * q^85 + 556 * q^86 - 132 * q^88 + 28 * q^89 - 520 * q^90 + 152 * q^92 - 72 * q^93 - 272 * q^94 - 704 * q^96 - 180 * q^97 - 568 * q^98

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.b.a	$44$	$3$	44.b	4.b	$2$	$10$	$10$	$1.199$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓	✓	44.3.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{6}q^{3}+\beta _{1}q^{4}+\beta _{7}q^{5}+\cdots\)