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

• Label: 960.2.o
• Level: $960$
• Weight: $2$
• Character orbit: 960.o
• Rep. character: $\chi_{960}(959,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	216	52	164
Cusp forms	168	44	124
Eisenstein series	48	8	40

Trace form

\( 44 q - 4 q^{9} + 16 q^{21} - 4 q^{25} + 16 q^{45} + 12 q^{49} - 8 q^{61} + 40 q^{69} - 20 q^{81} + 24 q^{85}+O(q^{100}) \)

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.o.a	$960$	$2$	960.o	60.h	$2$	$4$	$4$	$7.666$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)					60.2.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}-3q^{9}+\beta _{3}q^{15}+\cdots\)
960.2.o.b	$960$	$2$	960.o	60.h	$2$	$4$	$4$	$7.666$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)					240.2.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
960.2.o.c	$960$	$2$	960.o	60.h	$2$	$4$	$4$	$7.666$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)					60.2.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
960.2.o.d	$960$	$2$	960.o	60.h	$2$	$8$	$8$	$7.666$	\(\Q(\zeta_{24})\)	None					240.2.o.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{3}+\beta_1 q^{5}+(\beta_{4}-\beta_1+1)q^{9}+\cdots\)
960.2.o.e	$960$	$2$	960.o	60.h	$2$	$24$	$24$	$7.666$		None			✓		480.2.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(960, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)