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

• Label: 714.2.ba
• Level: $714$
• Weight: $2$
• Character orbit: 714.ba
• Rep. character: $\chi_{714}(319,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.ba (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	608	96	512
Cusp forms	544	96	448
Eisenstein series	64	0	64

Trace form

\( 96 q + 48 q^{4} - 8 q^{5} - 8 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
714.2.ba.a	$714$	$2$	714.ba	119.n	$12$	$8$	$2$	$5.701$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)
714.2.ba.b	$714$	$2$	714.ba	119.n	$12$	$8$	$2$	$5.701$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{2}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{4}q^{4}+(-1+\cdots)q^{5}+\cdots\)
714.2.ba.c	$714$	$2$	714.ba	119.n	$12$	$8$	$2$	$5.701$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{2}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{5}q^{5}+\cdots\)
714.2.ba.d	$714$	$2$	714.ba	119.n	$12$	$16$	$4$	$5.701$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{4}q^{2}-\beta _{13}q^{3}+\beta _{9}q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
714.2.ba.e	$714$	$2$	714.ba	119.n	$12$	$24$	$6$	$5.701$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$
714.2.ba.f	$714$	$2$	714.ba	119.n	$12$	$32$	$8$	$5.701$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)