Space of modular forms of level 222, weight 2, and Character 222.j

• Label: 222.2.j
• Level: $222$
• Weight: $2$
• Character orbit: 222.j
• Rep. character: $\chi_{222}(85,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(76\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(222, [\chi])\).

	Total	New	Old
Modular forms	84	12	72
Cusp forms	68	12	56
Eisenstein series	16	0	16

Trace form

\( 12 q + 2 q^{3} + 6 q^{4} + 2 q^{7} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(222, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
222.2.j.a	$222$	$2$	222.j	37.e	$6$	$4$	$2$	$1.773$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
222.2.j.b	$222$	$2$	222.j	37.e	$6$	$8$	$4$	$1.773$	8.0.303595776.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{4}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(222, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(222, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)