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

• Label: 666.2.j
• Level: $666$
• Weight: $2$
• Character orbit: 666.j
• Rep. character: $\chi_{666}(179,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $228$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(228\)
Trace bound:			\(5\)
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	244	20	224
Cusp forms	212	20	192
Eisenstein series	32	0	32

Trace form

\( 20 q + O(q^{10}) \)

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.j.a	$666$	$2$	666.j	111.g	$4$	$4$	$2$	$5.318$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{5}+\cdots\)
666.2.j.b	$666$	$2$	666.j	111.g	$4$	$4$	$2$	$5.318$	\(\Q(\zeta_{8})\)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-4q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
666.2.j.c	$666$	$2$	666.j	111.g	$4$	$4$	$2$	$5.318$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2+2\zeta_{8}^{2})q^{5}+\cdots\)
666.2.j.d	$666$	$2$	666.j	111.g	$4$	$8$	$4$	$5.318$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{4}+(1-\beta _{2}+\beta _{7})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \)