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

• Label: 714.2.m
• Level: $714$
• Weight: $2$
• Character orbit: 714.m
• Rep. character: $\chi_{714}(421,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $5$
• 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.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
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	304	40	264
Cusp forms	272	40	232
Eisenstein series	32	0	32

Trace form

\( 40 q - 40 q^{4} - 8 q^{5} + O(q^{10}) \)

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.m.a	$714$	$2$	714.m	17.c	$4$	$4$	$2$	$5.701$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(-2+\zeta_{8}+\cdots)q^{5}+\cdots\)
714.2.m.b	$714$	$2$	714.m	17.c	$4$	$4$	$2$	$5.701$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
714.2.m.c	$714$	$2$	714.m	17.c	$4$	$8$	$4$	$5.701$	8.0.836829184.2	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}-\beta _{1}q^{3}-q^{4}+(1+\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
714.2.m.d	$714$	$2$	714.m	17.c	$4$	$12$	$6$	$5.701$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{7}q^{2}+\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}-\beta _{3}q^{6}+\cdots\)
714.2.m.e	$714$	$2$	714.m	17.c	$4$	$12$	$6$	$5.701$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{9}q^{2}+\beta _{5}q^{3}-q^{4}+(-\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)