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

• Label: 720.2.o
• Level: $720$
• Weight: $2$
• Character orbit: 720.o
• Rep. character: $\chi_{720}(719,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	168	12	156
Cusp forms	120	12	108
Eisenstein series	48	0	48

Trace form

\( 12 q + 24 q^{25} + 60 q^{49} + 24 q^{61} - 60 q^{85}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
720.2.o.a	$720$	$2$	720.o	60.h	$2$	$4$	$4$	$5.749$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			720.2.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta_{3} q^{5}+2\beta_1 q^{13}+(-2\beta_{3}+\beta_{2})q^{17}+\cdots\)
720.2.o.b	$720$	$2$	720.o	60.h	$2$	$8$	$8$	$5.749$	\(\Q(\zeta_{24})\)	None		✓	✓		720.2.o.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}-\beta_1)q^{5}-\beta_{6} q^{7}+\beta_{3} q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(720, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)