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

• Label: 1584.2.cd
• Level: $1584$
• Weight: $2$
• Character orbit: 1584.cd
• Rep. character: $\chi_{1584}(17,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.cd (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1248	96	1152
Cusp forms	1056	96	960
Eisenstein series	192	0	192

Trace form

\( 96 q + O(q^{10}) \)

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.cd.a	$1584$	$2$	1584.cd	33.f	$10$	$8$	$2$	$12.648$	8.0.64000000.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}+\beta _{2}-\beta _{6}-\beta _{7})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
1584.2.cd.b	$1584$	$2$	1584.cd	33.f	$10$	$8$	$2$	$12.648$	8.0.64000000.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{6}-\beta _{7})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
1584.2.cd.c	$1584$	$2$	1584.cd	33.f	$10$	$16$	$4$	$12.648$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}+\beta _{10}-\beta _{12}-2\beta _{13})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1584.2.cd.d	$1584$	$2$	1584.cd	33.f	$10$	$16$	$4$	$12.648$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta _{4}+2\beta _{5}+\beta _{13}-\beta _{15})q^{5}+(1+\cdots)q^{7}+\cdots\)
1584.2.cd.e	$1584$	$2$	1584.cd	33.f	$10$	$24$	$6$	$12.648$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
1584.2.cd.f	$1584$	$2$	1584.cd	33.f	$10$	$24$	$6$	$12.648$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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