Space of modular forms of level 342, weight 3, and Character 342.bd

• Label: 342.3.bd
• Level: $342$
• Weight: $3$
• Character orbit: 342.bd
• Rep. character: $\chi_{342}(13,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	342.bd (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(342, [\chi])\).

	Total	New	Old
Modular forms	744	240	504
Cusp forms	696	240	456
Eisenstein series	48	0	48

Trace form

\( 240 q - 6 q^{3} + 12 q^{6} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(342, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
342.3.bd.a	$342$	$3$	342.bd	171.ae	$18$	$240$	$40$	$9.319$		None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)