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

• Label: 1944.1.m
• Level: $1944$
• Weight: $1$
• Character orbit: 1944.m
• Rep. character: $\chi_{1944}(161,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $324$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1944.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(324\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	100	4	96
Cusp forms	28	4	24
Eisenstein series	72	0	72

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

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

Trace form

\( 4 q - 2 q^{13} - 4 q^{19} + 2 q^{25} + 2 q^{31} - 2 q^{43} + 2 q^{49} - 8 q^{55} - 2 q^{61} + 2 q^{67} + 4 q^{73} - 2 q^{79} - 4 q^{85} + 2 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1944.1.m.a	$1944$	$1$	1944.m	9.d	$6$	$4$	$2$	$0.970$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		✓	✓	✓	1944.1.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{3})q^{5}-\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1944, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 2}\)