Space of modular forms of level 384, weight 1, and Character 384.h

• Label: 384.1.h
• Level: $384$
• Weight: $1$
• Character orbit: 384.h
• Rep. character: $\chi_{384}(65,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	384.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(384, [\chi])\).

	Total	New	Old
Modular forms	22	2	20
Cusp forms	6	2	4
Eisenstein series	16	0	16

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

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

Trace form

\( 2 q + 2 q^{9} - 2 q^{25} - 4 q^{33} - 2 q^{49} - 4 q^{73} + 2 q^{81} + 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(384, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
384.1.h.a	$384$	$1$	384.h	24.h	$2$	$1$	$1$	$0.192$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{3}) \)	✓	✓			384.1.h.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{3}+q^{9}+2q^{11}-q^{25}-q^{27}+\cdots\)
384.1.h.b	$384$	$1$	384.h	24.h	$2$	$1$	$1$	$0.192$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{3}) \)	✓	✓			384.1.h.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{9}-2q^{11}-q^{25}+q^{27}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(384, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)