Space of modular forms of level 714, weight 2, and Character 714.w

• Label: 714.2.w
• Level: $714$
• Weight: $2$
• Character orbit: 714.w
• Rep. character: $\chi_{714}(83,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $192$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.w (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 357 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).

	Total	New	Old
Modular forms	608	192	416
Cusp forms	544	192	352
Eisenstein series	64	0	64

Trace form

192 * q - 64 * q^15 - 192 * q^16 + 32 * q^18 + 16 * q^37 - 16 * q^39 - 24 * q^42 - 16 * q^43 - 32 * q^46 + 32 * q^49 + 48 * q^51 + 48 * q^58 - 64 * q^60 + 24 * q^63 + 32 * q^70 + 32 * q^78 + 64 * q^79 + 16 * q^84 + 208 * q^85 - 16 * q^88 + 32 * q^91 - 144 * q^93 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
714.2.w.a	$714$	$2$	714.w	357.w	$8$	$8$	$2$	$5.701$	\(\Q(\zeta_{16})\)	None		✓			714.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{2}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}+\cdots\)
714.2.w.b	$714$	$2$	714.w	357.w	$8$	$8$	$2$	$5.701$	\(\Q(\zeta_{16})\)	None		✓			714.2.w.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{2}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}+\cdots\)
714.2.w.c	$714$	$2$	714.w	357.w	$8$	$8$	$2$	$5.701$	\(\Q(\zeta_{16})\)	None		✓			714.2.w.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{2}q^{2}+(\zeta_{16}-\zeta_{16}^{3}-\zeta_{16}^{7})q^{3}+\cdots\)
714.2.w.d	$714$	$2$	714.w	357.w	$8$	$8$	$2$	$5.701$	\(\Q(\zeta_{16})\)	None		✓			714.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{2}q^{2}+(\zeta_{16}-\zeta_{16}^{3}-\zeta_{16}^{7})q^{3}+\cdots\)
714.2.w.e	$714$	$2$	714.w	357.w	$8$	$80$	$20$	$5.701$		None		✓			714.2.w.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{8}]$
714.2.w.f	$714$	$2$	714.w	357.w	$8$	$80$	$20$	$5.701$		None		✓			714.2.w.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(714, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)