Space of modular forms of level 1098, weight 2, and Character 1098.bd

• Label: 1098.2.bd
• Level: $1098$
• Weight: $2$
• Character orbit: 1098.bd
• Rep. character: $\chi_{1098}(143,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $372$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1098.bd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 183 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(372\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1098, [\chi])\).

	Total	New	Old
Modular forms	776	88	688
Cusp forms	712	88	624
Eisenstein series	64	0	64

Trace form

\( 88 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1098, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1098.2.bd.a	$1098$	$2$	1098.bd	183.o	$12$	$40$	$10$	$8.768$		None		✓			1098.2.bd.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$
1098.2.bd.b	$1098$	$2$	1098.bd	183.o	$12$	$48$	$12$	$8.768$		None		✓	✓		1098.2.bd.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1098, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1098, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(183, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(366, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(549, [\chi])\)\(^{\oplus 2}\)