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

• Label: 960.2.bf
• Level: $960$
• Weight: $2$
• Character orbit: 960.bf
• Rep. character: $\chi_{960}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bf (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 240 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	416	104	312
Cusp forms	352	88	264
Eisenstein series	64	16	48

Trace form

88 * q + 4 * q^3 - 8 * q^13 + 4 * q^15 - 8 * q^19 - 4 * q^21 + 4 * q^27 + 16 * q^31 - 4 * q^33 - 8 * q^37 + 24 * q^39 + 8 * q^45 + 4 * q^51 - 12 * q^57 - 24 * q^61 + 32 * q^63 + 12 * q^69 + 36 * q^75 - 8 * q^81 + 16 * q^85 - 12 * q^87 + 8 * q^91 - 16 * q^93 - 8 * q^97 - 32 * q^99

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.bf.a	$960$	$2$	960.bf	240.af	$4$	$88$	$44$	$7.666$		None			✓	✓	240.2.bb.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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