Space of modular forms of level 960, weight 4, and Character 960.f

• Label: 960.4.f
• Level: $960$
• Weight: $4$
• Character orbit: 960.f
• Rep. character: $\chi_{960}(769,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $21$
• Sturm bound: $768$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	960.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(768\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(960, [\chi])\).

	Total	New	Old
Modular forms	600	72	528
Cusp forms	552	72	480
Eisenstein series	48	0	48

Trace form

\( 72 q - 648 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(960, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.4.f.a	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+(-5+10i)q^{5}+4iq^{7}+\cdots\)
960.4.f.b	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+(-5-10i)q^{5}+4iq^{7}+\cdots\)
960.4.f.c	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(-2+11i)q^{5}+2iq^{7}+\cdots\)
960.4.f.d	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(-2-11i)q^{5}+2iq^{7}+\cdots\)
960.4.f.e	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(2+11i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.f	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(2-11i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.g	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(10-5i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.h	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+(10-5i)q^{5}+18iq^{7}-9q^{9}+\cdots\)
960.4.f.i	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+(10+5i)q^{5}+22iq^{7}-9q^{9}+\cdots\)
960.4.f.j	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+(10-5i)q^{5}+22iq^{7}-9q^{9}+\cdots\)
960.4.f.k	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+(10+5i)q^{5}+18iq^{7}-9q^{9}+\cdots\)
960.4.f.l	$960$	$4$	960.f	5.b	$2$	$2$	$2$	$56.642$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(10+5i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.m	$960$	$4$	960.f	5.b	$2$	$4$	$4$	$56.642$	\(\Q(i, \sqrt{89})\)	None		$4$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(-6-\beta _{2})q^{5}-22\beta _{1}q^{7}+\cdots\)
960.4.f.n	$960$	$4$	960.f	5.b	$2$	$4$	$4$	$56.642$	\(\Q(i, \sqrt{129})\)	None		$2$	$0$	\(0\)	\(0\)	\(-22\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(-5+5\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.o	$960$	$4$	960.f	5.b	$2$	$4$	$4$	$56.642$	\(\Q(i, \sqrt{129})\)	None		$2$	$0$	\(0\)	\(0\)	\(-22\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(-5-6\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.p	$960$	$4$	960.f	5.b	$2$	$4$	$4$	$56.642$	\(\Q(i, \sqrt{41})\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-1+\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
960.4.f.q	$960$	$4$	960.f	5.b	$2$	$4$	$4$	$56.642$	\(\Q(i, \sqrt{41})\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.r	$960$	$4$	960.f	5.b	$2$	$6$	$6$	$56.642$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+(10\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.s	$960$	$4$	960.f	5.b	$2$	$6$	$6$	$56.642$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{3}+(-2-\beta _{1}-\beta _{4})q^{5}+(10\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.t	$960$	$4$	960.f	5.b	$2$	$8$	$8$	$56.642$	8.0.\(\cdots\).9	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(-2+\beta _{4})q^{5}+(4\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
960.4.f.u	$960$	$4$	960.f	5.b	$2$	$8$	$8$	$56.642$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(2^{4}\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)