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

• Label: 798.2.cf
• Level: $798$
• Weight: $2$
• Character orbit: 798.cf
• Rep. character: $\chi_{798}(29,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $240$
• Newform subspaces: $4$
• Sturm bound: $320$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cf (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(320\)
Trace bound:			\(5\)
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	240	768
Cusp forms	912	240	672
Eisenstein series	96	0	96

Trace form

\( 240 q - 6 q^{3} - 6 q^{6} + 6 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
798.2.cf.a	$798$	$2$	798.cf	57.j	$18$	$60$	$10$	$6.372$		None		$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(-30\)		$\mathrm{SU}(2)[C_{18}]$
798.2.cf.b	$798$	$2$	798.cf	57.j	$18$	$60$	$10$	$6.372$		None		$2$	$0$	\(0\)	\(-3\)	\(3\)	\(30\)		$\mathrm{SU}(2)[C_{18}]$
798.2.cf.c	$798$	$2$	798.cf	57.j	$18$	$60$	$10$	$6.372$		None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(30\)		$\mathrm{SU}(2)[C_{18}]$
798.2.cf.d	$798$	$2$	798.cf	57.j	$18$	$60$	$10$	$6.372$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-30\)		$\mathrm{SU}(2)[C_{18}]$

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

\( S_{2}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)