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

• Label: 666.2.be
• Level: $666$
• Weight: $2$
• Character orbit: 666.be
• Rep. character: $\chi_{666}(125,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $228$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(228\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	488	40	448
Cusp forms	424	40	384
Eisenstein series	64	0	64

Trace form

\( 40 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
666.2.be.a	$666$	$2$	666.be	111.m	$12$	$8$	$2$	$5.318$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots\)
666.2.be.b	$666$	$2$	666.be	111.m	$12$	$8$	$2$	$5.318$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(2\zeta_{24}^{3}+2\zeta_{24}^{7})q^{5}+\cdots\)
666.2.be.c	$666$	$2$	666.be	111.m	$12$	$8$	$2$	$5.318$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots\)
666.2.be.d	$666$	$2$	666.be	111.m	$12$	$16$	$4$	$5.318$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{10}q^{2}-\beta _{9}q^{4}+(\beta _{1}+\beta _{7})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)