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

• Label: 798.2.m
• Level: $798$
• Weight: $2$
• Character orbit: 798.m
• Rep. character: $\chi_{798}(145,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $320$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	336	56	280
Cusp forms	304	56	248
Eisenstein series	32	0	32

Trace form

\( 56 q - 56 q^{4} - 4 q^{7} - 28 q^{9} + O(q^{10}) \)

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.m.a	$798$	$2$	798.m	133.i	$6$	$28$	$14$	$6.372$		None		$2$	$0$	\(0\)	\(-14\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$
798.2.m.b	$798$	$2$	798.m	133.i	$6$	$28$	$14$	$6.372$		None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{6}]$

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

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