Space of modular forms of level 342, weight 10, and Character 342.b

• Label: 342.10.b
• Level: $342$
• Weight: $10$
• Character orbit: 342.b
• Rep. character: $\chi_{342}(341,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $600$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(600\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(342, [\chi])\).

	Total	New	Old
Modular forms	548	60	488
Cusp forms	532	60	472
Eisenstein series	16	0	16

Trace form

\( 60 q + 15360 q^{4} + 3192 q^{7} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(342, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
342.10.b.a	$342$	$10$	342.b	57.d	$2$	$30$	$30$	$176.142$		None		✓			342.10.b.a	$2$	$0$	\(-480\)	\(0\)	\(0\)	\(1596\)		$\mathrm{SU}(2)[C_{2}]$
342.10.b.b	$342$	$10$	342.b	57.d	$2$	$30$	$30$	$176.142$		None		✓			342.10.b.a	$2$	$0$	\(480\)	\(0\)	\(0\)	\(1596\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{10}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)