Space of modular forms of level 444, weight 1, and Character 444.bf

• Label: 444.1.bf
• Level: $444$
• Weight: $1$
• Character orbit: 444.bf
• Rep. character: $\chi_{444}(53,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	444.bf (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(444, [\chi])\).

	Total	New	Old
Modular forms	42	6	36
Cusp forms	6	6	0
Eisenstein series	36	0	36

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 3 q^{7} + 6 q^{13} - 3 q^{21} - 3 q^{27} - 3 q^{37} - 3 q^{39} - 3 q^{49} - 3 q^{67} + 6 q^{75} - 3 q^{79} - 3 q^{91} - 3 q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(444, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
444.1.bf.a	$444$	$1$	444.bf	111.p	$18$	$6$	$1$	$0.222$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	444.1.bf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$		\(q+\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{3}-\zeta_{18}^{7})q^{7}+\cdots\)