Space of modular forms of level 360, weight 2, and Character 360.m

• Label: 360.2.m
• Level: $360$
• Weight: $2$
• Character orbit: 360.m
• Rep. character: $\chi_{360}(179,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(360, [\chi])\).

	Total	New	Old
Modular forms	80	24	56
Cusp forms	64	24	40
Eisenstein series	16	0	16

Trace form

\( 24 q - 4 q^{4} - 8 q^{10} + 20 q^{16} + 16 q^{19} - 32 q^{34} - 28 q^{40} - 48 q^{46} + 24 q^{49} - 28 q^{64} + 32 q^{70} - 56 q^{76} - 8 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(360, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
360.2.m.a	$360$	$2$	360.m	120.m	$2$	$4$	$4$	$2.875$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		✓			360.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
360.2.m.b	$360$	$2$	360.m	120.m	$2$	$4$	$4$	$2.875$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		✓			360.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots\)
360.2.m.c	$360$	$2$	360.m	120.m	$2$	$16$	$16$	$2.875$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		360.2.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

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