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

• Label: 960.2.h
• Level: $960$
• Weight: $2$
• Character orbit: 960.h
• Rep. character: $\chi_{960}(191,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $384$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(384\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	216	32	184
Cusp forms	168	32	136
Eisenstein series	48	0	48

Trace form

\( 32 q + O(q^{10}) \)

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	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.2.h.a	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	\(\Q(\zeta_{8})\)	None			480.2.h.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
960.2.h.b	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	\(\Q(\zeta_{8})\)	None			480.2.h.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}+\cdots\)
960.2.h.c	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	\(\Q(i, \sqrt{6})\)	None			240.2.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots\)
960.2.h.d	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	\(\Q(\zeta_{12})\)	None			240.2.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)
960.2.h.e	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	\(\Q(\zeta_{8})\)	None			480.2.h.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
960.2.h.f	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	\(\Q(\zeta_{8})\)	None			480.2.h.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
960.2.h.g	$960$	$2$	960.h	12.b	$2$	$8$	$8$	$7.666$	8.0.342102016.5	None			60.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{1}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\beta _{6}q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(960, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)