Space of modular forms of level 864, weight 3, and Character 864.h

• Label: 864.3.h
• Level: $864$
• Weight: $3$
• Character orbit: 864.h
• Rep. character: $\chi_{864}(593,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	864.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(432\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).

	Total	New	Old
Modular forms	312	32	280
Cusp forms	264	32	232
Eisenstein series	48	0	48

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.3.h.a	$864$	$3$	864.h	24.h	$2$	$2$	$2$	$23.542$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-10\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta )q^{5}+(-5-\beta )q^{7}+(-5+\cdots)q^{11}+\cdots\)
864.3.h.b	$864$	$3$	864.h	24.h	$2$	$2$	$2$	$23.542$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-10\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta )q^{5}+(-5+\beta )q^{7}+(5+2\beta )q^{11}+\cdots\)
864.3.h.c	$864$	$3$	864.h	24.h	$2$	$6$	$6$	$23.542$	6.0.121670000.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(10\)	$2^{9}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots\)
864.3.h.d	$864$	$3$	864.h	24.h	$2$	$6$	$6$	$23.542$	6.0.121670000.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(10\)	$2^{9}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{11}+\cdots\)
864.3.h.e	$864$	$3$	864.h	24.h	$2$	$8$	$8$	$23.542$	8.0.\(\cdots\).11	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-48\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(-6+\beta _{7})q^{7}+\beta _{3}q^{11}+\cdots\)
864.3.h.f	$864$	$3$	864.h	24.h	$2$	$8$	$8$	$23.542$	8.0.629407744.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(48\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+2\beta _{3})q^{5}+(6-\beta _{5})q^{7}+(-4\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)