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

• Label: 666.2.e
• Level: $666$
• Weight: $2$
• Character orbit: 666.e
• Rep. character: $\chi_{666}(223,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $228$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(228\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	236	72	164
Cusp forms	220	72	148
Eisenstein series	16	0	16

Trace form

72 * q + 2 * q^2 + 2 * q^3 - 36 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^8 - 10 * q^9 - 10 * q^11 - 4 * q^12 + 4 * q^14 + 4 * q^15 - 36 * q^16 + 12 * q^17 + 12 * q^18 + 12 * q^19 + 4 * q^20 - 24 * q^21 - 6 * q^22 - 8 * q^23 + 6 * q^24 - 36 * q^25 + 16 * q^26 + 8 * q^27 + 24 * q^29 + 24 * q^30 + 2 * q^32 + 38 * q^33 - 6 * q^34 - 24 * q^35 + 2 * q^36 - 14 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 - 6 * q^43 + 20 * q^44 - 40 * q^45 + 24 * q^46 - 20 * q^47 + 2 * q^48 - 48 * q^49 + 6 * q^50 + 26 * q^51 - 32 * q^53 - 6 * q^54 - 24 * q^55 + 4 * q^56 - 10 * q^57 + 12 * q^58 - 22 * q^59 - 8 * q^60 - 12 * q^61 + 20 * q^63 + 72 * q^64 - 16 * q^65 - 6 * q^67 - 6 * q^68 - 32 * q^69 - 24 * q^71 - 6 * q^72 + 12 * q^73 + 10 * q^74 + 44 * q^75 - 6 * q^76 + 32 * q^77 + 6 * q^78 - 12 * q^79 - 8 * q^80 - 2 * q^81 + 12 * q^82 + 50 * q^83 - 24 * q^85 - 6 * q^86 + 12 * q^87 - 6 * q^88 + 32 * q^89 + 4 * q^90 + 48 * q^91 - 8 * q^92 - 72 * q^93 - 12 * q^94 + 4 * q^95 - 6 * q^97 - 20 * q^98 + 44 * q^99

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.e.a	$666$	$2$	666.e	9.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		✓			666.2.e.a	$2$	$1$	\(-1\)	\(0\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.b	$666$	$2$	666.e	9.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		✓			666.2.e.b	$2$	$0$	\(1\)	\(3\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.c	$666$	$2$	666.e	9.c	$3$	$12$	$6$	$5.318$	12.0.\(\cdots\).1	None		✓			666.2.e.c	$2$	$0$	\(-6\)	\(2\)	\(5\)	\(5\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{11})q^{3}+\cdots\)
666.2.e.d	$666$	$2$	666.e	9.c	$3$	$14$	$7$	$5.318$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			666.2.e.d	$2$	$0$	\(7\)	\(-1\)	\(-3\)	\(3\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{10})q^{2}+\beta _{2}q^{3}+\beta _{10}q^{4}-\beta _{12}q^{5}+\cdots\)
666.2.e.e	$666$	$2$	666.e	9.c	$3$	$20$	$10$	$5.318$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			666.2.e.e	$2$	$0$	\(-10\)	\(2\)	\(-1\)	\(-1\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{11}q^{2}+\beta _{7}q^{3}+(-1+\beta _{11})q^{4}+\cdots\)
666.2.e.f	$666$	$2$	666.e	9.c	$3$	$22$	$11$	$5.318$		None		✓	✓		666.2.e.f	$2$	$0$	\(11\)	\(-4\)	\(1\)	\(-5\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(666, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)