Space of modular forms of level 702, weight 2, and Character 702.g

• Label: 702.2.g
• Level: $702$
• Weight: $2$
• Character orbit: 702.g
• Rep. character: $\chi_{702}(451,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $252$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(252\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(702, [\chi])\).

	Total	New	Old
Modular forms	276	28	248
Cusp forms	228	28	200
Eisenstein series	48	0	48

Trace form

28 * q - 14 * q^4 + 8 * q^7 - 8 * q^11 - 2 * q^13 + 8 * q^14 - 14 * q^16 + 8 * q^17 + 2 * q^19 - 8 * q^23 - 14 * q^25 - 4 * q^26 - 4 * q^28 + 10 * q^29 + 2 * q^31 + 12 * q^35 + 2 * q^37 + 18 * q^38 - 16 * q^41 - 4 * q^43 + 16 * q^44 + 40 * q^47 + 36 * q^49 - 8 * q^50 + 4 * q^52 + 8 * q^53 - 16 * q^56 - 16 * q^59 - 28 * q^61 + 16 * q^62 + 28 * q^64 + 46 * q^65 - 28 * q^67 - 16 * q^68 + 12 * q^71 - 28 * q^73 - 36 * q^74 - 4 * q^76 + 4 * q^77 - 10 * q^79 + 12 * q^82 - 42 * q^83 + 8 * q^86 - 4 * q^89 - 4 * q^91 + 4 * q^92 + 32 * q^95 + 44 * q^97 - 24 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(702, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
702.2.g.a	$702$	$2$	702.g	117.f	$3$	$2$	$1$	$5.605$	\(\Q(\sqrt{-3}) \)	None					234.2.f.a	$2$	$1$	\(-1\)	\(0\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
702.2.g.b	$702$	$2$	702.g	117.f	$3$	$2$	$1$	$5.605$	\(\Q(\sqrt{-3}) \)	None					234.2.f.b	$2$	$0$	\(1\)	\(0\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{7}+\cdots\)
702.2.g.c	$702$	$2$	702.g	117.f	$3$	$12$	$6$	$5.605$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					234.2.f.c	$2$	$0$	\(-6\)	\(0\)	\(3\)	\(-2\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{8}q^{2}+(-1-\beta _{8})q^{4}+\beta _{5}q^{5}+\beta _{11}q^{7}+\cdots\)
702.2.g.d	$702$	$2$	702.g	117.f	$3$	$12$	$6$	$5.605$	12.0.\(\cdots\).1	None					234.2.f.d	$2$	$0$	\(6\)	\(0\)	\(-1\)	\(10\)	$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(702, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(702, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)