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

• Label: 342.2.bb
• Level: $342$
• Weight: $2$
• Character orbit: 342.bb
• Rep. character: $\chi_{342}(53,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bb (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	408	48	360
Cusp forms	312	48	264
Eisenstein series	96	0	96

Trace form

\( 48 q + 48 q^{19} + 24 q^{22} + 72 q^{25} + 24 q^{34} - 72 q^{46} - 72 q^{49} - 120 q^{55} - 48 q^{58} - 120 q^{61} - 24 q^{64} - 96 q^{70} + 48 q^{79} + 24 q^{82} - 48 q^{91}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
342.2.bb.a	$342$	$2$	342.bb	57.j	$18$	$24$	$4$	$2.731$		None		✓			342.2.bb.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
342.2.bb.b	$342$	$2$	342.bb	57.j	$18$	$24$	$4$	$2.731$		None		✓			342.2.bb.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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