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

• Label: 342.2.s
• Level: $342$
• Weight: $2$
• Character orbit: 342.s
• Rep. character: $\chi_{342}(107,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• 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.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	136	8	128
Cusp forms	104	8	96
Eisenstein series	32	0	32

Trace form

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

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.s.a	$342$	$2$	342.s	57.f	$6$	$4$	$2$	$2.731$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
342.2.s.b	$342$	$2$	342.s	57.f	$6$	$4$	$2$	$2.731$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)

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

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