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

• Label: 960.2.f
• Level: $960$
• Weight: $2$
• Character orbit: 960.f
• Rep. character: $\chi_{960}(769,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $11$
• Sturm bound: $384$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(384\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	216	24	192
Cusp forms	168	24	144
Eisenstein series	48	0	48

Trace form

\( 24 q - 24 q^{9} - 8 q^{25} + 16 q^{41} - 24 q^{49} - 16 q^{61} - 16 q^{65} + 16 q^{69} + 24 q^{81} + 48 q^{85} + 16 q^{89}+O(q^{100}) \)

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	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.2.f.a	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					120.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
960.2.f.b	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					120.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
960.2.f.c	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					60.2.d.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i-1)q^{5}+4 i q^{7}+\cdots\)
960.2.f.d	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					480.2.f.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-2 i-1)q^{5}+4 i q^{7}+\cdots\)
960.2.f.e	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					480.2.f.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(2 i-1)q^{5}+4 i q^{7}-q^{9}+\cdots\)
960.2.f.f	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					60.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(2 i-1)q^{5}+4 i q^{7}-q^{9}+\cdots\)
960.2.f.g	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					480.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i+2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
960.2.f.h	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					30.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(i+2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
960.2.f.i	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					30.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-i+2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
960.2.f.j	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	\(\Q(\sqrt{-1}) \)	None					480.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i+2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
960.2.f.k	$960$	$2$	960.f	5.b	$2$	$4$	$4$	$7.666$	\(\Q(i, \sqrt{5})\)	None			✓		480.2.f.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+2\beta _{1}q^{7}-q^{9}+2\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(960, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)