Space of modular forms of level 1944, weight 1, and Character 1944.r

• Label: 1944.1.r
• Level: $1944$
• Weight: $1$
• Character orbit: 1944.r
• Rep. character: $\chi_{1944}(379,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $324$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1944.r (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 216 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(324\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1944, [\chi])\).

	Total	New	Old
Modular forms	162	72	90
Cusp forms	54	24	30
Eisenstein series	108	48	60

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1944, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1944.1.r.a	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{3}q^{8}+\cdots\)
1944.1.r.b	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{3}q^{8}+\cdots\)
1944.1.r.c	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)
1944.1.r.d	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1944, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1944, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)