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

• Label: 1444.1.h
• Level: $1444$
• Weight: $1$
• Character orbit: 1444.h
• Rep. character: $\chi_{1444}(69,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• 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.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
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	66	6	60
Cusp forms	6	6	0
Eisenstein series	60	0	60

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	4	0

Trace form

\( 6 q - q^{5} + 2 q^{7} + q^{9} + O(q^{10}) \)

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.h.a	$1444$	$1$	1444.h	19.d	$6$	$2$	$1$	$0.721$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$		\(q-\zeta_{6}^{2}q^{5}-q^{7}-\zeta_{6}q^{9}-q^{11}-\zeta_{6}^{2}q^{17}+\cdots\)
1444.1.h.b	$1444$	$1$	1444.h	19.d	$6$	$4$	$2$	$0.721$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$1$		\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)