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

• Label: 960.2.bc
• Level: $960$
• Weight: $2$
• Character orbit: 960.bc
• Rep. character: $\chi_{960}(367,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bc (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
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	416	48	368
Cusp forms	352	48	304
Eisenstein series	64	0	64

Trace form

\( 48 q - 48 q^{9} + O(q^{10}) \)

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.bc.a	$960$	$2$	960.bc	80.j	$4$	$2$	$1$	$7.666$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{3}+(-2+i)q^{5}+(-3-3i)q^{7}+\cdots\)
960.2.bc.b	$960$	$2$	960.bc	80.j	$4$	$2$	$1$	$7.666$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{3}+(-2-i)q^{5}+(-3-3i)q^{7}+\cdots\)
960.2.bc.c	$960$	$2$	960.bc	80.j	$4$	$2$	$1$	$7.666$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{3}+(-2+i)q^{5}+(1+i)q^{7}-q^{9}+\cdots\)
960.2.bc.d	$960$	$2$	960.bc	80.j	$4$	$6$	$3$	$7.666$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(2\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(2-\beta _{1})q^{5}-\beta _{5}q^{7}-q^{9}+\cdots\)
960.2.bc.e	$960$	$2$	960.bc	80.j	$4$	$16$	$8$	$7.666$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(4\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{3}+(-1+\beta _{10}+\beta _{11})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
960.2.bc.f	$960$	$2$	960.bc	80.j	$4$	$20$	$10$	$7.666$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(4\)	$2^{17}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{3}-\beta _{12}q^{5}+\beta _{1}q^{7}-q^{9}-\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)