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 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 6 * q^16 + 8 * q^21 + 6 * q^25 - 2 * q^27 - 4 * q^28 - 12 * q^30 - 4 * q^33 - 16 * q^34 - 6 * q^36 - 18 * q^37 + 12 * q^38 - 4 * q^40 - 36 * q^41 + 8 * q^44 + 12 * q^46 + 32 * q^47 - 2 * q^48 + 42 * q^49 - 44 * q^53 + 4 * q^58 + 28 * q^62 + 4 * q^63 - 6 * q^64 - 8 * q^65 - 16 * q^70 - 8 * q^71 - 40 * q^73 - 4 * q^74 - 2 * q^75 + 48 * q^77 - 4 * q^78 + 6 * q^81 + 16 * q^83 - 8 * q^84 + 8 * q^85 - 4 * q^86 + 4 * q^90 - 16 * q^95 - 8 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
222.2.c.a	$222$	$2$	222.c	37.b	$2$	$2$	$2$	$1.773$	\(\Q(\sqrt{-1}) \)	None		✓			222.2.c.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}-q^{4}+2 i q^{5}+i q^{6}+\cdots\)
222.2.c.b	$222$	$2$	222.c	37.b	$2$	$4$	$4$	$1.773$	\(\Q(i, \sqrt{65})\)	None		✓	✓		222.2.c.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{3}-q^{4}-2\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)

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

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