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

• Label: 960.2.m
• Level: $960$
• Weight: $2$
• Character orbit: 960.m
• Rep. character: $\chi_{960}(479,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	216	48	168
Cusp forms	168	48	120
Eisenstein series	48	0	48

Trace form

\( 48 q + 48 q^{49} + 48 q^{81}+O(q^{100}) \)

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.m.a	$960$	$2$	960.m	120.m	$2$	$8$	$8$	$7.666$	8.0.12960000.1	\(\Q(\sqrt{-30}) \)		✓			960.2.m.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}-\beta _{1}q^{5}-3q^{9}-\beta _{6}q^{11}+\cdots\)
960.2.m.b	$960$	$2$	960.m	120.m	$2$	$8$	$8$	$7.666$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-6}) \)		✓			960.2.m.b	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_1 q^{3}-\beta_{3} q^{5}+(-2\beta_{4}-\beta_{2})q^{7}+\cdots\)
960.2.m.c	$960$	$2$	960.m	120.m	$2$	$16$	$16$	$7.666$	16.0.\(\cdots\).9	None		✓			960.2.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{11}q^{5}+\beta _{1}q^{7}+(-\beta _{9}+\cdots)q^{9}+\cdots\)
960.2.m.d	$960$	$2$	960.m	120.m	$2$	$16$	$16$	$7.666$	16.0.\(\cdots\).9	None		✓			960.2.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}-\beta _{10}q^{5}+\beta _{1}q^{7}+(\beta _{7}+\beta _{12}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(960, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)