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

• Label: 1444.1.j
• Level: $1444$
• Weight: $1$
• Character orbit: 1444.j
• Rep. character: $\chi_{1444}(333,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $190$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1444.j (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(190\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	198	18	180
Cusp forms	18	18	0
Eisenstein series	180	0	180

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	12	0

Trace form

\( 18 q - 3 q^{7} + O(q^{10}) \)

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.j.a	$1444$	$1$	1444.j	19.f	$18$	$6$	$1$	$0.721$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q-\zeta_{18}^{8}q^{5}+\zeta_{18}^{3}q^{7}+\zeta_{18}^{4}q^{9}+\cdots\)
1444.1.j.b	$1444$	$1$	1444.j	19.f	$18$	$12$	$2$	$0.721$	12.0.\(\cdots\).1	$S_{4}$	None	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$		\(q+(-\beta _{5}+\beta _{11})q^{3}+(\beta _{2}-\beta _{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)