Space of modular forms of level 720, weight 3, and Character 720.l

• Label: 720.3.l
• Level: $720$
• Weight: $3$
• Character orbit: 720.l
• Rep. character: $\chi_{720}(161,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	720.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(720, [\chi])\).

	Total	New	Old
Modular forms	312	16	296
Cusp forms	264	16	248
Eisenstein series	48	0	48

Trace form

\( 16 q + 32 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(720, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
720.3.l.a	$720$	$3$	720.l	3.b	$2$	$4$	$4$	$19.619$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-7\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\)
720.3.l.b	$720$	$3$	720.l	3.b	$2$	$4$	$4$	$19.619$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{3}q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
720.3.l.c	$720$	$3$	720.l	3.b	$2$	$4$	$4$	$19.619$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(4-\beta _{3})q^{7}+(-\beta _{1}+6\beta _{2}+\cdots)q^{11}+\cdots\)
720.3.l.d	$720$	$3$	720.l	3.b	$2$	$4$	$4$	$19.619$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(32\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(8+\beta _{3})q^{7}+(\beta _{1}-6\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)