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

• Label: 1444.1.g
• Level: $1444$
• Weight: $1$
• Character orbit: 1444.g
• Rep. character: $\chi_{1444}(1151,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• 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.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
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	48	40	8
Cusp forms	8	8	0
Eisenstein series	40	32	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 4 q^{4} + 2 q^{5} - 4 q^{9} + O(q^{10}) \)

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.g.a	$1444$	$1$	1444.g	76.g	$6$	$4$	$2$	$0.721$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(-1-\beta _{3})q^{2}+\beta _{3}q^{4}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
1444.1.g.b	$1444$	$1$	1444.g	76.g	$6$	$4$	$2$	$0.721$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(2\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)