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

• Label: 714.2.p
• Level: $714$
• Weight: $2$
• Character orbit: 714.p
• Rep. character: $\chi_{714}(341,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	304	88	216
Cusp forms	272	88	184
Eisenstein series	32	0	32

Trace form

\( 88 q + 44 q^{4} + 20 q^{7} + 4 q^{9} + O(q^{10}) \)

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.p.a	$714$	$2$	714.p	21.g	$6$	$44$	$22$	$5.701$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{6}]$
714.2.p.b	$714$	$2$	714.p	21.g	$6$	$44$	$22$	$5.701$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)