Space of modular forms of level 342, weight 3, and Character 342.m

• Label: 342.3.m
• Level: $342$
• Weight: $3$
• Character orbit: 342.m
• Rep. character: $\chi_{342}(145,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	342.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(342, [\chi])\).

	Total	New	Old
Modular forms	256	36	220
Cusp forms	224	36	188
Eisenstein series	32	0	32

Trace form

\( 36 q + 36 q^{4} + 2 q^{5} + 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(342, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
342.3.m.a	$342$	$3$	342.m	19.d	$6$	$4$	$2$	$9.319$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
342.3.m.b	$342$	$3$	342.m	19.d	$6$	$8$	$4$	$9.319$	8.0.\(\cdots\).10	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-24\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{6}q^{2}+2\beta _{4}q^{4}+(-1+\beta _{1}+2\beta _{3}+\cdots)q^{5}+\cdots\)
342.3.m.c	$342$	$3$	342.m	19.d	$6$	$8$	$4$	$9.319$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}+(2-2\beta _{4})q^{4}+(\beta _{2}+2\beta _{4}+\cdots)q^{5}+\cdots\)
342.3.m.d	$342$	$3$	342.m	19.d	$6$	$16$	$8$	$9.319$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{2}+(2+2\beta _{1})q^{4}+(-\beta _{10}-\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)