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

• Label: 798.2.u
• Level: $798$
• Weight: $2$
• Character orbit: 798.u
• Rep. character: $\chi_{798}(647,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $320$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(320\)
Trace bound:			\(14\)
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	96	240
Cusp forms	304	96	208
Eisenstein series	32	0	32

Trace form

96 * q + 48 * q^4 + 4 * q^7 + 12 * q^9 + 12 * q^10 - 16 * q^15 - 48 * q^16 - 8 * q^18 - 12 * q^21 - 8 * q^22 - 12 * q^24 - 44 * q^25 - 4 * q^28 + 8 * q^30 - 12 * q^31 + 36 * q^33 + 24 * q^36 + 14 * q^39 + 12 * q^40 + 22 * q^42 + 16 * q^43 + 12 * q^45 + 16 * q^46 - 4 * q^49 - 40 * q^51 - 18 * q^54 - 20 * q^58 - 8 * q^60 + 72 * q^61 - 74 * q^63 - 96 * q^64 - 48 * q^66 + 24 * q^67 - 52 * q^70 + 8 * q^72 - 48 * q^73 - 60 * q^75 + 64 * q^78 - 4 * q^79 + 28 * q^81 + 48 * q^82 + 12 * q^84 + 112 * q^85 + 12 * q^87 - 4 * q^88 - 40 * q^91 - 40 * q^93 - 12 * q^96 + 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.u.a	$798$	$2$	798.u	21.g	$6$	$48$	$24$	$6.372$		None		✓			798.2.u.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$
798.2.u.b	$798$	$2$	798.u	21.g	$6$	$48$	$24$	$6.372$		None		✓			798.2.u.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(798, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)