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

• Label: 1944.1.h
• Level: $1944$
• Weight: $1$
• Character orbit: 1944.h
• Rep. character: $\chi_{1944}(485,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $324$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1944.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(324\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	34	10	24
Cusp forms	16	10	6
Eisenstein series	18	0	18

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	4	0

Trace form

\( 10 q + 6 q^{4} + 4 q^{7} + O(q^{10}) \)

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	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.h.a	$1944$	$1$	1944.h	24.h	$2$	$3$	$3$	$0.970$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-6}) \)	None	✓	✓			1944.1.h.a	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
1944.1.h.b	$1944$	$1$	1944.h	24.h	$2$	$3$	$3$	$0.970$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-6}) \)	None	✓	✓			1944.1.h.a	$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
1944.1.h.c	$1944$	$1$	1944.h	24.h	$2$	$4$	$4$	$0.970$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓	✓		1944.1.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)

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

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