Space of modular forms of level 1444, weight 1, and Character 1444.b

• Label: 1444.1.b
• Level: $1444$
• Weight: $1$
• Character orbit: 1444.b
• Rep. character: $\chi_{1444}(723,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $190$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1444.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(190\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1444, [\chi])\).

	Total	New	Old
Modular forms	24	21	3
Cusp forms	4	4	0
Eisenstein series	20	17	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 4 q^{4} - 2 q^{5} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1444, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1444.1.b.a	$1444$	$1$	1444.b	4.b	$2$	$2$	$2$	$0.721$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+q^{9}+\cdots\)
1444.1.b.b	$1444$	$1$	1444.b	4.b	$2$	$2$	$2$	$0.721$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+q^{9}+\cdots\)