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

• Label: 342.2.n
• Level: $342$
• Weight: $2$
• Character orbit: 342.n
• Rep. character: $\chi_{342}(293,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	128	40	88
Cusp forms	112	40	72
Eisenstein series	16	0	16

Trace form

\( 40 q + 40 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \)

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.n.a	$342$	$2$	342.n	171.t	$6$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{5}+\cdots\)
342.2.n.b	$342$	$2$	342.n	171.t	$6$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(2\)	\(-3\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)
342.2.n.c	$342$	$2$	342.n	171.t	$6$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
342.2.n.d	$342$	$2$	342.n	171.t	$6$	$8$	$4$	$2.731$	8.0.764411904.5	None		$2$	$0$	\(8\)	\(0\)	\(12\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
342.2.n.e	$342$	$2$	342.n	171.t	$6$	$8$	$4$	$2.731$	8.0.152695449.1	None		$2$	$0$	\(8\)	\(4\)	\(-9\)	\(6\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(\beta _{3}-\beta _{6})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
342.2.n.f	$342$	$2$	342.n	171.t	$6$	$18$	$9$	$2.731$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-18\)	\(-1\)	\(3\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q-q^{2}+\beta _{14}q^{3}+q^{4}-\beta _{10}q^{5}-\beta _{14}q^{6}+\cdots\)

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

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