Space of modular forms of level 360, weight 3, and Character 360.l

• Label: 360.3.l
• Level: $360$
• Weight: $3$
• Character orbit: 360.l
• Rep. character: $\chi_{360}(161,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	360.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(360, [\chi])\).

	Total	New	Old
Modular forms	160	8	152
Cusp forms	128	8	120
Eisenstein series	32	0	32

Trace form

\( 8 q - 32 q^{7} + 16 q^{13} + 64 q^{19} - 40 q^{25} - 48 q^{31} - 16 q^{37} + 32 q^{43} - 56 q^{49} + 80 q^{55} + 176 q^{61} + 32 q^{67} - 208 q^{73} - 176 q^{79} - 304 q^{91} + 432 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(360, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
360.3.l.a	$360$	$3$	360.l	3.b	$2$	$4$	$4$	$9.809$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			360.3.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-32\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-8+\beta _{3})q^{7}+(-\beta _{1}-6\beta _{2}+\cdots)q^{11}+\cdots\)
360.3.l.b	$360$	$3$	360.l	3.b	$2$	$4$	$4$	$9.809$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			360.3.l.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{3}q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(360, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)