Space of modular forms of level 1584, weight 3, and Character 1584.i

• Label: 1584.3.i
• Level: $1584$
• Weight: $3$
• Character orbit: 1584.i
• Rep. character: $\chi_{1584}(881,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $5$
• Sturm bound: $864$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1584.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(864\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1584, [\chi])\).

	Total	New	Old
Modular forms	600	40	560
Cusp forms	552	40	512
Eisenstein series	48	0	48

Trace form

\( 40 q + 32 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1584, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1584.3.i.a	$1584$	$3$	1584.i	3.b	$2$	$4$	$4$	$43.161$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-2\beta _{1}q^{7}+\beta _{3}q^{11}+(-4+\cdots)q^{13}+\cdots\)
1584.3.i.b	$1584$	$3$	1584.i	3.b	$2$	$8$	$8$	$43.161$	8.0.\(\cdots\).6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{7})q^{7}-\beta _{5}q^{11}+\cdots\)
1584.3.i.c	$1584$	$3$	1584.i	3.b	$2$	$8$	$8$	$43.161$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}+(2+\beta _{5})q^{7}+\beta _{3}q^{11}+(-1+\cdots)q^{13}+\cdots\)
1584.3.i.d	$1584$	$3$	1584.i	3.b	$2$	$8$	$8$	$43.161$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}+\beta _{5})q^{5}+(2-\beta _{2}+\beta _{4})q^{7}+\cdots\)
1584.3.i.e	$1584$	$3$	1584.i	3.b	$2$	$12$	$12$	$43.161$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{6})q^{7}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)