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

• Label: 1584.2.b
• Level: $1584$
• Weight: $2$
• Character orbit: 1584.b
• Rep. character: $\chi_{1584}(593,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	312	24	288
Cusp forms	264	24	240
Eisenstein series	48	0	48

Trace form

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

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1584.2.b.a	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+(-3-\beta )q^{11}-3\beta q^{13}+\cdots\)
1584.2.b.b	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+3\beta q^{7}+(-3+\beta )q^{11}+6q^{17}+\cdots\)
1584.2.b.c	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-3\beta q^{7}+(3+\beta )q^{11}-6q^{17}+\cdots\)
1584.2.b.d	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+(3-\beta )q^{11}+3\beta q^{13}+6q^{17}+\cdots\)
1584.2.b.e	$1584$	$2$	1584.b	33.d	$2$	$4$	$4$	$12.648$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\)
1584.2.b.f	$1584$	$2$	1584.b	33.d	$2$	$6$	$6$	$12.648$	6.0.12781568.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots\)
1584.2.b.g	$1584$	$2$	1584.b	33.d	$2$	$6$	$6$	$12.648$	6.0.12781568.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \)