Space of modular forms of level 360, weight 4, and Character 360.m

• Label: 360.4.m
• Level: $360$
• Weight: $4$
• Character orbit: 360.m
• Rep. character: $\chi_{360}(179,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).

	Total	New	Old
Modular forms	224	72	152
Cusp forms	208	72	136
Eisenstein series	16	0	16

Trace form

\( 72 q + 12 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
360.4.m.a	$360$	$4$	360.m	120.m	$2$	$4$	$4$	$21.241$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-104\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta _{1}q^{2}-8q^{4}+5\beta _{2}q^{5}+(-26+\cdots)q^{7}+\cdots\)
360.4.m.b	$360$	$4$	360.m	120.m	$2$	$4$	$4$	$21.241$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(104\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta _{1}q^{2}-8q^{4}-5\beta _{2}q^{5}+(26-\beta _{3})q^{7}+\cdots\)
360.4.m.c	$360$	$4$	360.m	120.m	$2$	$64$	$64$	$21.241$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)