Space of modular forms of level 882, weight 3, and Character 882.b

• Label: 882.3.b
• Level: $882$
• Weight: $3$
• Character orbit: 882.b
• Rep. character: $\chi_{882}(197,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $9$
• Sturm bound: $504$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(504\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(882, [\chi])\).

	Total	New	Old
Modular forms	368	26	342
Cusp forms	304	26	278
Eisenstein series	64	0	64

Trace form

\( 26 q - 52 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(882, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.3.b.a	$882$	$3$	882.b	3.b	$2$	$2$	$2$	$24.033$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
882.3.b.b	$882$	$3$	882.b	3.b	$2$	$2$	$2$	$24.033$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
882.3.b.c	$882$	$3$	882.b	3.b	$2$	$2$	$2$	$24.033$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots\)
882.3.b.d	$882$	$3$	882.b	3.b	$2$	$2$	$2$	$24.033$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-2q^{4}+\beta q^{5}+2\beta q^{8}+2q^{10}+\cdots\)
882.3.b.e	$882$	$3$	882.b	3.b	$2$	$2$	$2$	$24.033$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
882.3.b.f	$882$	$3$	882.b	3.b	$2$	$4$	$4$	$24.033$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{1}q^{8}+\cdots\)
882.3.b.g	$882$	$3$	882.b	3.b	$2$	$4$	$4$	$24.033$	\(\Q(\sqrt{-2}, \sqrt{37})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
882.3.b.h	$882$	$3$	882.b	3.b	$2$	$4$	$4$	$24.033$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
882.3.b.i	$882$	$3$	882.b	3.b	$2$	$4$	$4$	$24.033$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-2q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)