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

• Label: 222.2.c
• Level: $222$
• Weight: $2$
• Character orbit: 222.c
• Rep. character: $\chi_{222}(73,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(76\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	42	6	36
Cusp forms	34	6	28
Eisenstein series	8	0	8

Trace form

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

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.c.a	$222$	$2$	222.c	37.b	$2$	$2$	$2$	$1.773$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
222.2.c.b	$222$	$2$	222.c	37.b	$2$	$4$	$4$	$1.773$	\(\Q(i, \sqrt{65})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{3}-q^{4}-2\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)

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

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