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

• Label: 720.2.f
• Level: $720$
• Weight: $2$
• Character orbit: 720.f
• Rep. character: $\chi_{720}(289,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $7$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	168	16	152
Cusp forms	120	14	106
Eisenstein series	48	2	46

Trace form

\( 14 q + O(q^{10}) \)

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.f.a	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots\)
720.2.f.b	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}-2iq^{7}+2q^{11}+2iq^{13}+\cdots\)
720.2.f.c	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{5}-2iq^{7}-4q^{11}-2iq^{17}+\cdots\)
720.2.f.d	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+2\beta q^{17}+4q^{19}+4\beta q^{23}+\cdots\)
720.2.f.e	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+i)q^{5}+iq^{7}-4q^{11}+2iq^{13}+\cdots\)
720.2.f.f	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots\)
720.2.f.g	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+i)q^{5}-4iq^{7}+4q^{11}+4iq^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)