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

• Label: 342.3.d
• Level: $342$
• Weight: $3$
• Character orbit: 342.d
• Rep. character: $\chi_{342}(37,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	342.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
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	128	18	110
Cusp forms	112	18	94
Eisenstein series	16	0	16

Trace form

\( 18 q - 36 q^{4} - 2 q^{5} + 10 q^{7} + O(q^{10}) \)

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.d.a	$342$	$3$	342.d	19.b	$2$	$2$	$2$	$9.319$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-2q^{4}+q^{5}+5q^{7}+2\beta q^{8}+\cdots\)
342.3.d.b	$342$	$3$	342.d	19.b	$2$	$8$	$8$	$9.319$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-12\)	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}-\beta _{5}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
342.3.d.c	$342$	$3$	342.d	19.b	$2$	$8$	$8$	$9.319$	8.0.\(\cdots\).9	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}+\cdots\)

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

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