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

• Label: 660.2.k
• Level: $660$
• Weight: $2$
• Character orbit: 660.k
• Rep. character: $\chi_{660}(571,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	152	48	104
Cusp forms	136	48	88
Eisenstein series	16	0	16

Trace form

\( 48 q - 8 q^{4} - 48 q^{9} + O(q^{10}) \)

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.k.a	$660$	$2$	660.k	44.c	$2$	$4$	$4$	$5.270$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-2q^{4}-q^{5}+\zeta_{8}^{3}q^{6}+\cdots\)
660.2.k.b	$660$	$2$	660.k	44.c	$2$	$4$	$4$	$5.270$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots\)
660.2.k.c	$660$	$2$	660.k	44.c	$2$	$20$	$20$	$5.270$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
660.2.k.d	$660$	$2$	660.k	44.c	$2$	$20$	$20$	$5.270$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{17}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)