Space of modular forms of level 342, weight 2, and Character 342.b

• Label: 342.2.b
• Level: $342$
• Weight: $2$
• Character orbit: 342.b
• Rep. character: $\chi_{342}(341,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(342, [\chi])\).

	Total	New	Old
Modular forms	68	4	64
Cusp forms	52	4	48
Eisenstein series	16	0	16

Trace form

\( 4 q + 4 q^{4} + 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(342, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
342.2.b.a	$342$	$2$	342.b	57.d	$2$	$2$	$2$	$2.731$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots\)
342.2.b.b	$342$	$2$	342.b	57.d	$2$	$2$	$2$	$2.731$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)