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

• Label: 714.2.t
• Level: $714$
• Weight: $2$
• Character orbit: 714.t
• Rep. character: $\chi_{714}(67,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $7$
• 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.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	304	48	256
Cusp forms	272	48	224
Eisenstein series	32	0	32

Trace form

\( 48 q - 24 q^{4} + 24 q^{9} + O(q^{10}) \)

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.t.a	$714$	$2$	714.t	119.j	$6$	$4$	$2$	$5.701$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
714.2.t.b	$714$	$2$	714.t	119.j	$6$	$4$	$2$	$5.701$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
714.2.t.c	$714$	$2$	714.t	119.j	$6$	$4$	$2$	$5.701$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
714.2.t.d	$714$	$2$	714.t	119.j	$6$	$8$	$4$	$5.701$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{24}^{2})q^{2}+(-\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots\)
714.2.t.e	$714$	$2$	714.t	119.j	$6$	$8$	$4$	$5.701$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{24}^{4})q^{2}+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{3}+\cdots\)
714.2.t.f	$714$	$2$	714.t	119.j	$6$	$8$	$4$	$5.701$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{24}^{2})q^{2}+(-\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots\)
714.2.t.g	$714$	$2$	714.t	119.j	$6$	$12$	$6$	$5.701$	12.0.\(\cdots\).37	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{7})q^{2}-\beta _{4}q^{3}+\beta _{7}q^{4}-\beta _{5}q^{5}+\cdots\)

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

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