Space of modular forms of level 960, weight 3, and Character 960.e

• Label: 960.3.e
• Level: $960$
• Weight: $3$
• Character orbit: 960.e
• Rep. character: $\chi_{960}(511,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $5$
• Sturm bound: $576$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(576\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).

	Total	New	Old
Modular forms	408	32	376
Cusp forms	360	32	328
Eisenstein series	48	0	48

Trace form

\( 32 q - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.3.e.a	$960$	$3$	960.e	4.b	$2$	$4$	$4$	$26.158$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
960.3.e.b	$960$	$3$	960.e	4.b	$2$	$4$	$4$	$26.158$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
960.3.e.c	$960$	$3$	960.e	4.b	$2$	$8$	$8$	$26.158$	8.0.85100625.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(2\beta _{2}+\beta _{5})q^{7}-3q^{9}+\cdots\)
960.3.e.d	$960$	$3$	960.e	4.b	$2$	$8$	$8$	$26.158$	8.0.12960000.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-4\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
960.3.e.e	$960$	$3$	960.e	4.b	$2$	$8$	$8$	$26.158$	8.0.12960000.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(\beta _{3}-\beta _{5})q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)