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

• Label: 882.2.bb
• Level: $882$
• Weight: $2$
• Character orbit: 882.bb
• Rep. character: $\chi_{882}(25,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $672$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 441 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	2064	672	1392
Cusp forms	1968	672	1296
Eisenstein series	96	0	96

Trace form

672 * q - 112 * q^4 + 4 * q^5 - 10 * q^6 + 2 * q^7 - 10 * q^9 - 2 * q^13 - 2 * q^14 - 6 * q^15 - 112 * q^16 + 14 * q^17 + 8 * q^18 + 4 * q^19 + 4 * q^20 + 20 * q^21 - 78 * q^23 + 4 * q^24 + 56 * q^25 + 16 * q^26 + 84 * q^27 + 2 * q^28 - 26 * q^29 - 8 * q^30 + 4 * q^31 + 40 * q^33 + 14 * q^35 - 10 * q^36 + 26 * q^37 + 12 * q^38 - 16 * q^39 + 6 * q^41 - 86 * q^42 - 2 * q^43 + 214 * q^45 - 78 * q^46 + 30 * q^47 - 4 * q^49 + 8 * q^50 + 6 * q^51 + 26 * q^52 - 156 * q^53 - 14 * q^54 - 30 * q^55 - 2 * q^56 - 48 * q^57 + 78 * q^58 - 44 * q^59 - 6 * q^60 - 82 * q^61 - 44 * q^62 - 24 * q^63 - 112 * q^64 - 28 * q^65 + 16 * q^66 + 28 * q^67 - 42 * q^68 - 66 * q^69 + 18 * q^70 + 14 * q^71 + 8 * q^72 + 28 * q^73 + 6 * q^74 - 34 * q^75 + 4 * q^76 - 50 * q^77 - 8 * q^78 + 16 * q^79 - 24 * q^80 - 46 * q^81 + 376 * q^83 - 22 * q^84 - 4 * q^86 - 60 * q^87 + 106 * q^89 + 82 * q^90 + 16 * q^91 + 6 * q^92 + 76 * q^93 + 24 * q^94 + 52 * q^95 + 4 * q^96 - 2 * q^97 - 32 * q^98 - 190 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.2.bb.a	$882$	$2$	882.bb	441.y	$21$	$336$	$28$	$7.043$		None		✓			882.2.y.b	$2$	$0$	\(-56\)	\(-5\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
882.2.bb.b	$882$	$2$	882.bb	441.y	$21$	$336$	$28$	$7.043$		None		✓			882.2.y.a	$2$	$0$	\(56\)	\(5\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{21}]$

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

\( S_{2}^{\mathrm{old}}(882, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)