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

• Label: 342.2.g
• Level: $342$
• Weight: $2$
• Character orbit: 342.g
• Rep. character: $\chi_{342}(163,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(120\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	136	14	122
Cusp forms	104	14	90
Eisenstein series	32	0	32

Trace form

14 * q + q^2 - 7 * q^4 - 2 * q^5 + 4 * q^7 - 2 * q^8 - 2 * q^10 + 2 * q^11 + 6 * q^13 + 2 * q^14 - 7 * q^16 - 2 * q^17 - 11 * q^19 + 4 * q^20 - q^22 - 4 * q^23 - 5 * q^25 + 4 * q^26 - 2 * q^28 + 2 * q^29 + 16 * q^31 + q^32 - 14 * q^34 - 2 * q^40 + 27 * q^41 - 20 * q^43 - q^44 - 16 * q^46 + 26 * q^47 + 22 * q^49 - 54 * q^50 + 6 * q^52 - 6 * q^53 - 10 * q^55 - 4 * q^56 - 4 * q^58 - 29 * q^59 - 2 * q^61 - 4 * q^62 + 14 * q^64 - 64 * q^65 + 23 * q^67 + 4 * q^68 - 12 * q^70 - 6 * q^71 + 31 * q^73 + 28 * q^74 + 7 * q^76 + 76 * q^77 - 16 * q^79 - 2 * q^80 + 15 * q^82 + 2 * q^83 - 24 * q^85 + 32 * q^86 + 2 * q^88 + 10 * q^89 - 8 * q^91 - 4 * q^92 + 44 * q^94 + 32 * q^95 + 17 * q^97 + q^98

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.g.a	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None		✓			342.2.g.a	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
342.2.g.b	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None					38.2.c.a	$2$	$1$	\(-1\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}+q^{8}+\cdots\)
342.2.g.c	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None					114.2.e.b	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{7}+q^{8}+\cdots\)
342.2.g.d	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None					114.2.e.a	$2$	$0$	\(1\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
342.2.g.e	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	\(\Q(\sqrt{-3}) \)	None		✓			342.2.g.a	$2$	$0$	\(1\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
342.2.g.f	$342$	$2$	342.g	19.c	$3$	$4$	$2$	$2.731$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None			✓		38.2.c.b	$2$	$0$	\(2\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

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

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