Space of modular forms of level 738, weight 2, and Character 738.ba

• Label: 738.2.ba
• Level: $738$
• Weight: $2$
• Character orbit: 738.ba
• Rep. character: $\chi_{738}(17,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $224$
• Newform subspaces: $4$
• Sturm bound: $252$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 123 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(252\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(738, [\chi])\).

	Total	New	Old
Modular forms	2144	224	1920
Cusp forms	1888	224	1664
Eisenstein series	256	0	256

Trace form

\( 224 q + 24 q^{13} + 56 q^{16} + 32 q^{22} - 32 q^{37} + 64 q^{43} + 32 q^{46} - 64 q^{55} + 32 q^{58} - 72 q^{61} - 64 q^{67} + 160 q^{73} + 32 q^{76} + 160 q^{79} + 32 q^{85} + 256 q^{91} + 160 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(738, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
738.2.ba.a	$738$	$2$	738.ba	123.o	$40$	$48$	$3$	$5.893$		None		✓			738.2.ba.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$\mathrm{SU}(2)[C_{40}]$
738.2.ba.b	$738$	$2$	738.ba	123.o	$40$	$48$	$3$	$5.893$		None		✓			738.2.ba.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$\mathrm{SU}(2)[C_{40}]$
738.2.ba.c	$738$	$2$	738.ba	123.o	$40$	$64$	$4$	$5.893$		None		✓			738.2.ba.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{40}]$
738.2.ba.d	$738$	$2$	738.ba	123.o	$40$	$64$	$4$	$5.893$		None		✓			738.2.ba.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{40}]$

Decomposition of \(S_{2}^{\mathrm{old}}(738, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(738, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(246, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(369, [\chi])\)\(^{\oplus 2}\)