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

• Label: 342.2.u
• Level: $342$
• Weight: $2$
• Character orbit: 342.u
• Rep. character: $\chi_{342}(55,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $54$
• Newform subspaces: $7$
• Sturm bound: $120$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(120\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	408	54	354
Cusp forms	312	54	258
Eisenstein series	96	0	96

Trace form

54 * q - 6 * q^7 + 3 * q^8 - 6 * q^11 + 12 * q^13 + 12 * q^14 + 24 * q^17 - 30 * q^19 + 12 * q^20 + 24 * q^22 + 12 * q^23 - 24 * q^25 + 6 * q^26 - 6 * q^28 + 18 * q^29 + 6 * q^31 + 12 * q^34 + 24 * q^35 + 36 * q^37 - 3 * q^38 + 9 * q^41 + 42 * q^43 - 12 * q^44 - 24 * q^46 - 42 * q^47 - 39 * q^49 - 3 * q^50 - 6 * q^52 - 72 * q^53 - 54 * q^55 - 36 * q^56 - 24 * q^58 - 33 * q^59 - 66 * q^61 - 54 * q^62 - 27 * q^64 - 105 * q^67 - 9 * q^68 - 12 * q^70 - 42 * q^71 - 30 * q^73 - 18 * q^74 - 6 * q^76 - 12 * q^77 + 6 * q^79 + 27 * q^82 + 42 * q^83 + 120 * q^85 + 12 * q^86 - 6 * q^88 + 36 * q^89 + 84 * q^91 + 30 * q^92 + 36 * q^94 - 12 * q^95 + 3 * q^97 + 72 * 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.u.a	$342$	$2$	342.u	19.e	$9$	$6$	$1$	$2.731$	\(\Q(\zeta_{18})\)	None					114.2.i.d	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(-1+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
342.2.u.b	$342$	$2$	342.u	19.e	$9$	$6$	$1$	$2.731$	\(\Q(\zeta_{18})\)	None					114.2.i.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(-1+2\zeta_{18}+\cdots)q^{5}+\cdots\)
342.2.u.c	$342$	$2$	342.u	19.e	$9$	$6$	$1$	$2.731$	\(\Q(\zeta_{18})\)	None					38.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(-2\zeta_{18}+2\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
342.2.u.d	$342$	$2$	342.u	19.e	$9$	$6$	$1$	$2.731$	\(\Q(\zeta_{18})\)	None					114.2.i.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(1+2\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
342.2.u.e	$342$	$2$	342.u	19.e	$9$	$6$	$1$	$2.731$	\(\Q(\zeta_{18})\)	None					114.2.i.a	$2$	$0$	\(0\)	\(0\)	\(9\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
342.2.u.f	$342$	$2$	342.u	19.e	$9$	$12$	$2$	$2.731$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			342.2.u.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{8}q^{2}-\beta _{11}q^{4}+(\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
342.2.u.g	$342$	$2$	342.u	19.e	$9$	$12$	$2$	$2.731$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			342.2.u.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}-\beta _{11})q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)

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

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