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

• Label: 798.2.i
• Level: $798$
• Weight: $2$
• Character orbit: 798.i
• Rep. character: $\chi_{798}(163,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $4$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
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 - 28 * q^4 - 4 * q^5 + 4 * q^7 + 56 * q^9 + 8 * q^10 + 8 * q^13 - 20 * q^14 - 28 * q^16 - 24 * q^17 - 8 * q^19 + 8 * q^20 - 4 * q^21 + 24 * q^23 - 52 * q^25 - 8 * q^26 + 4 * q^28 - 4 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 20 * q^34 + 20 * q^35 - 28 * q^36 - 20 * q^37 + 24 * q^38 - 4 * q^39 + 8 * q^40 + 4 * q^41 - 4 * q^42 + 12 * q^43 - 4 * q^45 + 12 * q^46 + 8 * q^47 + 24 * q^49 - 16 * q^50 - 16 * q^52 + 20 * q^53 + 4 * q^55 + 16 * q^56 + 4 * q^58 - 48 * q^59 - 8 * q^61 - 8 * q^62 + 4 * q^63 + 56 * q^64 - 32 * q^65 - 24 * q^67 + 12 * q^68 - 40 * q^69 - 16 * q^70 + 40 * q^73 + 8 * q^74 + 4 * q^76 - 48 * q^77 + 8 * q^78 - 44 * q^79 - 4 * q^80 + 56 * q^81 - 32 * q^82 + 16 * q^83 + 8 * q^84 - 12 * q^85 + 16 * q^86 + 128 * q^89 + 8 * q^90 + 44 * q^91 - 12 * q^92 + 8 * q^93 + 36 * q^94 - 40 * q^95 + 16 * q^97 - 32 * q^98

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.i.a	$798$	$2$	798.i	133.g	$3$	$14$	$7$	$6.372$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			798.2.i.a	$2$	$0$	\(-7\)	\(-14\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{8})q^{2}-q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
798.2.i.b	$798$	$2$	798.i	133.g	$3$	$14$	$7$	$6.372$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			798.2.i.b	$2$	$0$	\(-7\)	\(14\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}+q^{3}+\beta _{3}q^{4}-\beta _{1}q^{5}+\cdots\)
798.2.i.c	$798$	$2$	798.i	133.g	$3$	$14$	$7$	$6.372$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			798.2.i.c	$2$	$0$	\(7\)	\(-14\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
798.2.i.d	$798$	$2$	798.i	133.g	$3$	$14$	$7$	$6.372$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			798.2.i.d	$2$	$0$	\(7\)	\(14\)	\(-2\)	\(-6\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{6})q^{2}+q^{3}-\beta _{6}q^{4}-\beta _{7}q^{5}+\cdots\)

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

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