Space of modular forms of level 864, weight 1, and Character 864.h

• Label: 864.1.h
• Level: $864$
• Weight: $1$
• Character orbit: 864.h
• Rep. character: $\chi_{864}(593,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	864.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(864, [\chi])\).

	Total	New	Old
Modular forms	32	2	30
Cusp forms	8	2	6
Eisenstein series	24	0	24

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

\( 2 q + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(864, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.1.h.a	$864$	$1$	864.h	24.h	$2$	$1$	$1$	$0.431$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-q^{5}+q^{7}+q^{11}+2q^{29}+q^{31}+\cdots\)
864.1.h.b	$864$	$1$	864.h	24.h	$2$	$1$	$1$	$0.431$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(1\)	\(1\)	$1$		\(q+q^{5}+q^{7}-q^{11}-2q^{29}+q^{31}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(864, [\chi]) \cong \)