Space of modular forms of level 864, weight 2, and Character 864.i

• Label: 864.2.i
• Level: $864$
• Weight: $2$
• Character orbit: 864.i
• Rep. character: $\chi_{864}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

	Total	New	Old
Modular forms	336	24	312
Cusp forms	240	24	216
Eisenstein series	96	0	96

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.2.i.a	$864$	$2$	864.i	9.c	$3$	$2$	$1$	$6.899$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
864.2.i.b	$864$	$2$	864.i	9.c	$3$	$2$	$1$	$6.899$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
864.2.i.c	$864$	$2$	864.i	9.c	$3$	$4$	$2$	$6.899$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
864.2.i.d	$864$	$2$	864.i	9.c	$3$	$4$	$2$	$6.899$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
864.2.i.e	$864$	$2$	864.i	9.c	$3$	$4$	$2$	$6.899$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{5}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(1+\cdots)q^{11}+\cdots\)
864.2.i.f	$864$	$2$	864.i	9.c	$3$	$8$	$4$	$6.899$	8.0.170772624.1	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{6}q^{5}+(\beta _{1}-\beta _{7})q^{7}-\beta _{3}q^{11}+(-2\beta _{4}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)