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

• Label: 660.2.c
• Level: $660$
• Weight: $2$
• Character orbit: 660.c
• Rep. character: $\chi_{660}(529,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	156	8	148
Cusp forms	132	8	124
Eisenstein series	24	0	24

Trace form

8 * q - 8 * q^9 + 8 * q^19 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 16 * q^31 - 8 * q^35 + 8 * q^39 + 8 * q^41 + 24 * q^49 + 48 * q^59 - 8 * q^65 + 16 * q^69 + 16 * q^75 - 56 * q^79 + 8 * q^81 - 24 * q^85 - 16 * q^89 - 16 * q^91 + 24 * q^95

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
660.2.c.a	$660$	$2$	660.c	5.b	$2$	$2$	$2$	$5.270$	\(\Q(\sqrt{-1}) \)	None		✓			660.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(2 i-1)q^{5}+2 i q^{7}-q^{9}+\cdots\)
660.2.c.b	$660$	$2$	660.c	5.b	$2$	$2$	$2$	$5.270$	\(\Q(\sqrt{-1}) \)	None		✓			660.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i+1)q^{5}-q^{9}+q^{11}+\cdots\)
660.2.c.c	$660$	$2$	660.c	5.b	$2$	$4$	$4$	$5.270$	\(\Q(i, \sqrt{5})\)	None		✓	✓		660.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(660, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)