Space of modular forms of level 960, weight 2, and Character 960.w

• Label: 960.2.w
• Level: $960$
• Weight: $2$
• Character orbit: 960.w
• Rep. character: $\chi_{960}(127,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).

	Total	New	Old
Modular forms	432	48	384
Cusp forms	336	48	288
Eisenstein series	96	0	96

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(960, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.2.w.a	$960$	$2$	960.w	20.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
960.2.w.b	$960$	$2$	960.w	20.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{3}q^{3}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+(1+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
960.2.w.c	$960$	$2$	960.w	20.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{3}q^{3}+(2+\zeta_{8}^{2})q^{5}+4\zeta_{8}q^{7}+\cdots\)
960.2.w.d	$960$	$2$	960.w	20.e	$4$	$8$	$4$	$7.666$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}^{5}q^{3}+(-1-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
960.2.w.e	$960$	$2$	960.w	20.e	$4$	$8$	$4$	$7.666$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
960.2.w.f	$960$	$2$	960.w	20.e	$4$	$8$	$4$	$7.666$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}+\beta _{4}q^{5}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
960.2.w.g	$960$	$2$	960.w	20.e	$4$	$12$	$6$	$7.666$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(\beta _{2}+\beta _{9})q^{7}+\beta _{7}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)