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

• Label: 864.3.e
• Level: $864$
• Weight: $3$
• Character orbit: 864.e
• Rep. character: $\chi_{864}(161,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $432$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	864.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(432\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\)

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.e.a	$864$	$3$	864.e	3.b	$2$	$4$	$4$	$23.542$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(-3+\beta _{1})q^{7}+(-\beta _{2}-3\beta _{3})q^{11}+\cdots\)
864.3.e.b	$864$	$3$	864.e	3.b	$2$	$4$	$4$	$23.542$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(-3-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
864.3.e.c	$864$	$3$	864.e	3.b	$2$	$4$	$4$	$23.542$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(3+\beta _{1})q^{7}+(\beta _{2}-3\beta _{3})q^{11}+\cdots\)
864.3.e.d	$864$	$3$	864.e	3.b	$2$	$4$	$4$	$23.542$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(3+\zeta_{8}^{3})q^{7}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
864.3.e.e	$864$	$3$	864.e	3.b	$2$	$8$	$8$	$23.542$	8.0.2441150464.4	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{5}+\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
864.3.e.f	$864$	$3$	864.e	3.b	$2$	$8$	$8$	$23.542$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{2}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)