Space of modular forms of level 660, weight 2, and Character 660.bg

• Label: 660.2.bg
• Level: $660$
• Weight: $2$
• Character orbit: 660.bg
• Rep. character: $\chi_{660}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $288$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.bg (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 220 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(660, [\chi])\).

	Total	New	Old
Modular forms	608	288	320
Cusp forms	544	288	256
Eisenstein series	64	0	64

Trace form

\( 288 q - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(660, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
660.2.bg.a	$660$	$2$	660.bg	220.o	$10$	$144$	$36$	$5.270$		None		$4$	$0$	\(0\)	\(-36\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
660.2.bg.b	$660$	$2$	660.bg	220.o	$10$	$144$	$36$	$5.270$		None		$4$	$0$	\(0\)	\(36\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(660, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)