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

• Label: 738.2.s
• Level: $738$
• Weight: $2$
• Character orbit: 738.s
• Rep. character: $\chi_{738}(133,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $336$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.s (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 369 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1040	336	704
Cusp forms	976	336	640
Eisenstein series	64	0	64

Trace form

336 * q + 2 * q^2 + 2 * q^3 + 42 * q^4 + 4 * q^5 - 11 * q^6 - 4 * q^8 + 6 * q^9 + 3 * q^11 - 4 * q^12 + 16 * q^14 + 12 * q^15 + 42 * q^16 + 28 * q^17 - 4 * q^18 - 18 * q^19 + 4 * q^20 + 56 * q^21 - 6 * q^22 + 18 * q^23 - 4 * q^24 + 42 * q^25 - 4 * q^27 - 6 * q^29 - 6 * q^30 - 8 * q^32 + 11 * q^33 - 6 * q^34 - 8 * q^35 - 11 * q^36 - 2 * q^38 - 52 * q^39 - 19 * q^41 + 64 * q^42 + 9 * q^43 + 4 * q^44 + 8 * q^45 + 24 * q^46 - 36 * q^47 - 3 * q^48 + 30 * q^49 - 24 * q^50 - 46 * q^51 + 152 * q^53 + 8 * q^54 - 4 * q^56 - 38 * q^57 - 50 * q^59 + 36 * q^60 + 18 * q^61 - 32 * q^62 - 20 * q^63 - 84 * q^64 - 28 * q^65 - 13 * q^66 + 9 * q^67 - 4 * q^68 + 24 * q^69 - 12 * q^70 - 68 * q^71 - 3 * q^72 + 12 * q^73 + 20 * q^74 + 29 * q^75 + 9 * q^76 + 26 * q^77 + 34 * q^78 - 8 * q^80 - 58 * q^81 - 18 * q^82 - 36 * q^83 - 10 * q^84 - 96 * q^85 - 22 * q^86 - 24 * q^87 - 6 * q^88 + 20 * q^89 + 88 * q^90 - 12 * q^92 - 8 * q^93 - 12 * q^94 - 10 * q^95 - 42 * q^97 - 84 * q^98 - 44 * q^99

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.s.a	$738$	$2$	738.s	369.s	$15$	$160$	$20$	$5.893$		None		✓			738.2.s.a	$4$	$0$	\(-20\)	\(-2\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{15}]$
738.2.s.b	$738$	$2$	738.s	369.s	$15$	$176$	$22$	$5.893$		None		✓	✓		738.2.s.b	$4$	$0$	\(22\)	\(4\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{15}]$

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

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