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

• Label: 798.2.p
• Level: $798$
• Weight: $2$
• Character orbit: 798.p
• Rep. character: $\chi_{798}(107,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $104$
• Newform subspaces: $4$
• Sturm bound: $320$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 399 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(320\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	336	104	232
Cusp forms	304	104	200
Eisenstein series	32	0	32

Trace form

104 * q + 104 * q^4 + 8 * q^7 + 12 * q^13 - 30 * q^15 + 104 * q^16 + 4 * q^19 + 12 * q^22 - 96 * q^25 + 8 * q^28 + 4 * q^30 + 12 * q^31 - 12 * q^34 - 10 * q^39 - 26 * q^42 + 20 * q^43 + 4 * q^45 + 20 * q^49 + 12 * q^52 + 12 * q^54 - 32 * q^55 - 38 * q^57 - 4 * q^58 - 30 * q^60 + 20 * q^61 + 28 * q^63 + 104 * q^64 + 16 * q^66 + 32 * q^73 + 30 * q^75 + 4 * q^76 - 12 * q^78 + 16 * q^81 - 16 * q^82 - 20 * q^85 + 80 * q^87 + 12 * q^88 - 48 * q^90 - 12 * q^91 + 88 * q^93 + 24 * q^94 - 12 * q^97 - 10 * 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.p.a	$798$	$2$	798.p	399.am	$6$	$2$	$1$	$6.372$	\(\Q(\sqrt{-3}) \)	None		✓			798.2.p.a	$2$	$0$	\(-2\)	\(3\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1-\zeta_{6})q^{6}+\cdots\)
798.2.p.b	$798$	$2$	798.p	399.am	$6$	$2$	$1$	$6.372$	\(\Q(\sqrt{-3}) \)	None		✓			798.2.p.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{6}+\cdots\)
798.2.p.c	$798$	$2$	798.p	399.am	$6$	$50$	$25$	$6.372$		None		✓			798.2.p.c	$2$	$0$	\(-50\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
798.2.p.d	$798$	$2$	798.p	399.am	$6$	$50$	$25$	$6.372$		None		✓			798.2.p.c	$2$	$0$	\(50\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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