Space of modular forms of level 882, weight 2, and Character 882.z

• Label: 882.2.z
• Level: $882$
• Weight: $2$
• Character orbit: 882.z
• Rep. character: $\chi_{882}(37,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $288$
• Newform subspaces: $8$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.z (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

	Total	New	Old
Modular forms	2112	288	1824
Cusp forms	1920	288	1632
Eisenstein series	192	0	192

Trace form

\( 288 q + 24 q^{4} - 4 q^{5} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.2.z.a	$882$	$2$	882.z	49.g	$21$	$24$	$2$	$7.043$		None		$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.b	$882$	$2$	882.z	49.g	$21$	$24$	$2$	$7.043$		None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.c	$882$	$2$	882.z	49.g	$21$	$24$	$2$	$7.043$		None		$2$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.d	$882$	$2$	882.z	49.g	$21$	$24$	$2$	$7.043$		None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.e	$882$	$2$	882.z	49.g	$21$	$36$	$3$	$7.043$		None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-1\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.f	$882$	$2$	882.z	49.g	$21$	$36$	$3$	$7.043$		None		$2$	$0$	\(3\)	\(0\)	\(-2\)	\(-5\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.g	$882$	$2$	882.z	49.g	$21$	$60$	$5$	$7.043$		None		$2$	$0$	\(-5\)	\(0\)	\(-3\)	\(1\)		$\mathrm{SU}(2)[C_{21}]$
882.2.z.h	$882$	$2$	882.z	49.g	$21$	$60$	$5$	$7.043$		None		$2$	$0$	\(5\)	\(0\)	\(3\)	\(1\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)