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

• Label: 702.2.b
• Level: $702$
• Weight: $2$
• Character orbit: 702.b
• Rep. character: $\chi_{702}(649,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $7$
• Sturm bound: $252$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(252\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	138	20	118
Cusp forms	114	20	94
Eisenstein series	24	0	24

Trace form

\( 20 q - 20 q^{4} - 16 q^{10} + 20 q^{16} - 4 q^{25} + 16 q^{40} - 16 q^{43} - 36 q^{49} - 8 q^{61} - 20 q^{64} + 12 q^{79} + 28 q^{82} + 40 q^{91} - 84 q^{94}+O(q^{100}) \)

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.b.a	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	\(\Q(\sqrt{-1}) \)	None		✓			702.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+3 i q^{7}-i q^{8}+3 i q^{11}+\cdots\)
702.2.b.b	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	\(\Q(\sqrt{-1}) \)	None		✓			702.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-i q^{8}-6 i q^{11}+(-3 i+2)q^{13}+\cdots\)
702.2.b.c	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	\(\Q(\sqrt{-1}) \)	None		✓			702.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-i q^{8}-6 i q^{11}+(3 i+2)q^{13}+\cdots\)
702.2.b.d	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	\(\Q(\sqrt{-1}) \)	None		✓			702.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-3 i q^{7}-i q^{8}+3 i q^{11}+\cdots\)
702.2.b.e	$702$	$2$	702.b	13.b	$2$	$4$	$4$	$5.605$	\(\Q(i, \sqrt{13})\)	None		✓			702.2.b.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}-2\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots\)
702.2.b.f	$702$	$2$	702.b	13.b	$2$	$4$	$4$	$5.605$	\(\Q(i, \sqrt{10})\)	None		✓			702.2.b.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
702.2.b.g	$702$	$2$	702.b	13.b	$2$	$4$	$4$	$5.605$	\(\Q(i, \sqrt{10})\)	None		✓			702.2.b.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(702, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)