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

• Label: 342.2.x
• Level: $342$
• Weight: $2$
• Character orbit: 342.x
• Rep. character: $\chi_{342}(29,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $120$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	384	120	264
Cusp forms	336	120	216
Eisenstein series	48	0	48

Trace form

120 * q - 6 * q^3 - 6 * q^6 + 6 * q^9 + 6 * q^13 + 48 * q^15 - 54 * q^17 - 36 * q^18 + 6 * q^19 - 9 * q^22 + 36 * q^23 + 3 * q^24 - 9 * q^27 + 6 * q^28 + 48 * q^33 + 6 * q^36 - 6 * q^39 - 6 * q^43 - 54 * q^45 - 3 * q^48 - 60 * q^49 - 144 * q^50 - 72 * q^51 + 12 * q^52 + 96 * q^57 - 90 * q^59 + 6 * q^60 + 42 * q^61 - 6 * q^63 - 60 * q^64 - 69 * q^66 + 102 * q^67 - 9 * q^68 - 3 * q^72 - 24 * q^73 + 12 * q^78 - 12 * q^79 + 6 * q^81 - 9 * q^82 - 72 * q^83 + 54 * q^84 - 54 * q^87 - 54 * q^89 + 78 * q^90 - 12 * q^91 - 6 * q^93 - 54 * q^95 + 18 * q^97 + 108 * q^98 + 39 * q^99

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.x.a	$342$	$2$	342.x	171.x	$18$	$12$	$2$	$2.731$	12.0.\(\cdots\).1	None		✓			342.2.x.a	$2$	$0$	\(0\)	\(6\)	\(9\)	\(-9\)	$3^{2}$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{9}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(\beta _{6}-\beta _{10}+\cdots)q^{4}+\cdots\)
342.2.x.b	$342$	$2$	342.x	171.x	$18$	$48$	$8$	$2.731$		None		✓			342.2.x.b	$2$	$0$	\(0\)	\(-6\)	\(-9\)	\(9\)		$\mathrm{SU}(2)[C_{18}]$
342.2.x.c	$342$	$2$	342.x	171.x	$18$	$60$	$10$	$2.731$		None		✓	✓		342.2.x.c	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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