Space of modular forms of level 760, weight 2, and Character 760.bl

• Label: 760.2.bl
• Level: $760$
• Weight: $2$
• Character orbit: 760.bl
• Rep. character: $\chi_{760}(501,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

	Total	New	Old
Modular forms	248	160	88
Cusp forms	232	160	72
Eisenstein series	16	0	16

Trace form

\( 160 q - 2 q^{4} - 2 q^{6} + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
760.2.bl.a	$760$	$2$	760.bl	152.p	$6$	$4$	$2$	$6.069$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
760.2.bl.b	$760$	$2$	760.bl	152.p	$6$	$4$	$2$	$6.069$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+3\zeta_{12}q^{3}+\cdots\)
760.2.bl.c	$760$	$2$	760.bl	152.p	$6$	$152$	$76$	$6.069$		None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(20\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)