Space of modular forms of level 378, weight 2, and Character 378.v

• Label: 378.2.v
• Level: $378$
• Weight: $2$
• Character orbit: 378.v
• Rep. character: $\chi_{378}(67,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $144$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 189 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(378, [\chi])\).

	Total	New	Old
Modular forms	456	144	312
Cusp forms	408	144	264
Eisenstein series	48	0	48

Trace form

144 * q + 6 * q^6 + 24 * q^9 + 24 * q^11 - 6 * q^14 - 12 * q^15 - 24 * q^17 - 30 * q^21 + 42 * q^23 - 36 * q^26 + 6 * q^29 + 18 * q^30 - 36 * q^33 - 36 * q^35 + 6 * q^36 - 72 * q^39 - 12 * q^41 + 48 * q^42 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 12 * q^50 - 36 * q^51 - 30 * q^53 - 36 * q^54 - 6 * q^56 - 6 * q^57 - 60 * q^59 + 18 * q^60 + 18 * q^61 - 48 * q^62 - 60 * q^63 - 72 * q^64 + 54 * q^65 + 18 * q^68 - 60 * q^69 - 18 * q^70 + 24 * q^71 - 12 * q^72 + 72 * q^73 - 36 * q^74 + 12 * q^75 - 30 * q^77 + 36 * q^78 - 36 * q^79 - 12 * q^80 + 48 * q^81 - 6 * q^84 + 72 * q^85 - 24 * q^86 - 156 * q^87 - 72 * q^89 + 36 * q^91 + 42 * q^92 - 96 * q^93 - 36 * q^94 - 30 * q^95 - 24 * q^98 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
378.2.v.a	$378$	$2$	378.v	189.u	$9$	$72$	$12$	$3.018$		None		✓			378.2.v.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$
378.2.v.b	$378$	$2$	378.v	189.u	$9$	$72$	$12$	$3.018$		None		✓			378.2.v.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(378, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)