Space of modular forms of level 666, weight 2, and Character 666.s

• Label: 666.2.s
• Level: $666$
• Weight: $2$
• Character orbit: 666.s
• Rep. character: $\chi_{666}(307,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $228$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(228\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

	Total	New	Old
Modular forms	244	28	216
Cusp forms	212	28	184
Eisenstein series	32	0	32

Trace form

28 * q + 14 * q^4 - 4 * q^10 - 8 * q^11 - 14 * q^16 - 4 * q^25 - 2 * q^34 - 14 * q^37 + 24 * q^38 - 2 * q^40 + 12 * q^41 - 4 * q^44 - 12 * q^46 + 32 * q^47 + 6 * q^49 - 8 * q^53 + 36 * q^55 + 2 * q^58 + 12 * q^59 - 30 * q^61 + 4 * q^62 - 28 * q^64 + 4 * q^65 + 4 * q^67 - 8 * q^70 - 8 * q^71 + 8 * q^73 + 20 * q^74 + 36 * q^77 + 24 * q^79 + 16 * q^83 + 28 * q^85 - 28 * q^86 - 24 * q^89 + 12 * q^91 - 12 * q^92 + 12 * q^94 + 56 * q^95 - 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
666.2.s.a	$666$	$2$	666.s	37.e	$6$	$4$	$2$	$5.318$	\(\Q(\zeta_{12})\)	None					74.2.e.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
666.2.s.b	$666$	$2$	666.s	37.e	$6$	$4$	$2$	$5.318$	\(\Q(\zeta_{12})\)	None		✓			666.2.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{8}+\cdots\)
666.2.s.c	$666$	$2$	666.s	37.e	$6$	$4$	$2$	$5.318$	\(\Q(\zeta_{12})\)	None		✓			666.2.s.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{5}+\cdots\)
666.2.s.d	$666$	$2$	666.s	37.e	$6$	$4$	$2$	$5.318$	\(\Q(\zeta_{12})\)	None					222.2.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
666.2.s.e	$666$	$2$	666.s	37.e	$6$	$4$	$2$	$5.318$	\(\Q(\zeta_{12})\)	None					74.2.e.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}^{2})q^{5}+\cdots\)
666.2.s.f	$666$	$2$	666.s	37.e	$6$	$8$	$4$	$5.318$	\(\Q(i, \sqrt{3}, \sqrt{11})\)	None			✓		222.2.j.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}+(1+\beta _{4})q^{4}+(-2\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)