Space of modular forms of level 1584, weight 2, and Character 1584.d

• Label: 1584.2.d
• Level: $1584$
• Weight: $2$
• Character orbit: 1584.d
• Rep. character: $\chi_{1584}(287,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

	Total	New	Old
Modular forms	312	20	292
Cusp forms	264	20	244
Eisenstein series	48	0	48

Trace form

\( 20 q - 16 q^{13} - 20 q^{25} - 8 q^{37} - 4 q^{49} + 40 q^{61} - 16 q^{73} + 24 q^{85} - 16 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1584.2.d.a	$1584$	$2$	1584.d	12.b	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-2}) \)	None		✓			1584.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}-q^{11}+\beta q^{17}-2\beta q^{19}+\cdots\)
1584.2.d.b	$1584$	$2$	1584.d	12.b	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-2}) \)	None		✓			1584.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2\beta q^{7}+q^{11}+\beta q^{17}+2\beta q^{19}+\cdots\)
1584.2.d.c	$1584$	$2$	1584.d	12.b	$2$	$8$	$8$	$12.648$	8.0.1768034304.5	None		✓			1584.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}-\beta _{4}q^{7}-q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots\)
1584.2.d.d	$1584$	$2$	1584.d	12.b	$2$	$8$	$8$	$12.648$	8.0.1768034304.5	None		✓			1584.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+\beta _{4}q^{7}+q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)