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

• Label: 360.2.b
• Level: $360$
• Weight: $2$
• Character orbit: 360.b
• Rep. character: $\chi_{360}(251,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	80	16	64
Cusp forms	64	16	48
Eisenstein series	16	0	16

Trace form

16 * q - 4 * q^4 + 4 * q^10 + 4 * q^16 + 16 * q^19 - 32 * q^22 + 16 * q^25 - 16 * q^28 - 24 * q^34 + 4 * q^40 - 16 * q^46 + 16 * q^49 - 8 * q^52 - 40 * q^58 - 4 * q^64 + 32 * q^67 - 24 * q^70 + 32 * q^73 + 24 * q^76 + 88 * q^82 - 32 * q^88 - 96 * q^91 + 88 * q^94 - 32 * q^97

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.b.a	$360$	$2$	360.b	24.f	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-2}) \)	None		✓			360.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.b	$360$	$2$	360.b	24.f	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-2}) \)	None		✓			360.2.b.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.c	$360$	$2$	360.b	24.f	$2$	$6$	$6$	$2.875$	6.0.2580992.1	None		✓			360.2.b.c	$2$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.b.d	$360$	$2$	360.b	24.f	$2$	$6$	$6$	$2.875$	6.0.2580992.1	None		✓			360.2.b.c	$2$	$0$	\(2\)	\(0\)	\(6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)