Space of modular forms of level 798, weight 2, and Character 798.bx

• Label: 798.2.bx
• Level: $798$
• Weight: $2$
• Character orbit: 798.bx
• Rep. character: $\chi_{798}(13,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $168$
• Newform subspaces: $2$
• Sturm bound: $320$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bx (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(320\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(798, [\chi])\).

	Total	New	Old
Modular forms	1008	168	840
Cusp forms	912	168	744
Eisenstein series	96	0	96

Trace form

168 * q - 12 * q^7 - 24 * q^11 + 24 * q^14 + 24 * q^21 - 12 * q^22 + 24 * q^23 + 12 * q^25 - 72 * q^29 + 60 * q^35 + 12 * q^42 - 120 * q^43 + 24 * q^44 - 36 * q^46 + 24 * q^49 - 24 * q^53 + 12 * q^57 + 84 * q^64 + 72 * q^65 - 96 * q^67 + 48 * q^71 - 120 * q^77 + 48 * q^78 + 96 * q^79 + 132 * q^85 + 48 * q^86 - 60 * q^91 + 48 * q^92 - 72 * q^93 + 48 * q^95 - 72 * q^98 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(798, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
798.2.bx.a	$798$	$2$	798.bx	133.aa	$18$	$84$	$14$	$6.372$		None		✓			798.2.bx.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$
798.2.bx.b	$798$	$2$	798.bx	133.aa	$18$	$84$	$14$	$6.372$		None		✓			798.2.bx.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(798, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(798, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)