Space of modular forms of level 720, weight 2, and Character 720.w

• Label: 720.2.w
• Level: $720$
• Weight: $2$
• Character orbit: 720.w
• Rep. character: $\chi_{720}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $288$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(288\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(720, [\chi])\).

	Total	New	Old
Modular forms	336	24	312
Cusp forms	240	24	216
Eisenstein series	96	0	96

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(720, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
720.2.w.a	$720$	$2$	720.w	15.e	$4$	$4$	$2$	$5.749$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-2-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
720.2.w.b	$720$	$2$	720.w	15.e	$4$	$4$	$2$	$5.749$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
720.2.w.c	$720$	$2$	720.w	15.e	$4$	$4$	$2$	$5.749$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-4\zeta_{8}-4\zeta_{8}^{3})q^{11}+\cdots\)
720.2.w.d	$720$	$2$	720.w	15.e	$4$	$4$	$2$	$5.749$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2+2\zeta_{8}^{2})q^{7}+(2\zeta_{8}+\cdots)q^{11}+\cdots\)
720.2.w.e	$720$	$2$	720.w	15.e	$4$	$8$	$4$	$5.749$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{5}+(1+\beta _{2}+\beta _{5})q^{7}+(\beta _{1}+\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)