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

• Label: 660.2.bl
• Level: $660$
• Weight: $2$
• Character orbit: 660.bl
• Rep. character: $\chi_{660}(41,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.bl (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	624	64	560
Cusp forms	528	64	464
Eisenstein series	96	0	96

Trace form

\( 64 q - 4 q^{3} - 2 q^{9} + O(q^{10}) \)

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.bl.a	$660$	$2$	660.bl	33.f	$10$	$16$	$4$	$5.270$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\beta _{2}-\beta _{8}+\beta _{10}-\beta _{12})q^{3}+\cdots\)
660.2.bl.b	$660$	$2$	660.bl	33.f	$10$	$48$	$12$	$5.270$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)