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

• Label: 960.2.v
• Level: $960$
• Weight: $2$
• Character orbit: 960.v
• Rep. character: $\chi_{960}(257,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $14$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	432	104	328
Cusp forms	336	88	248
Eisenstein series	96	16	80

Trace form

\( 88 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.2.v.a	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$2$	$1$	\(0\)	\(-4\)	\(-4\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}^{2})q^{3}+(-1-2\zeta_{8})q^{5}+\cdots\)
960.2.v.b	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
960.2.v.c	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
960.2.v.d	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
960.2.v.e	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
960.2.v.f	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(1+2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
960.2.v.g	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+(1+2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
960.2.v.h	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
960.2.v.i	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(-4\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8}^{2})q^{3}+(-1-2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
960.2.v.j	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
960.2.v.k	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
960.2.v.l	$960$	$2$	960.v	15.e	$4$	$4$	$2$	$7.666$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
960.2.v.m	$960$	$2$	960.v	15.e	$4$	$16$	$8$	$7.666$	16.0.\(\cdots\).9	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{10}q^{3}+\beta _{13}q^{5}+(\beta _{5}-\beta _{11})q^{7}+\cdots\)
960.2.v.n	$960$	$2$	960.v	15.e	$4$	$24$	$12$	$7.666$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)