Space of modular forms of level 333, weight 2, and Character 333.c

• Label: 333.2.c
• Level: $333$
• Weight: $2$
• Character orbit: 333.c
• Rep. character: $\chi_{333}(73,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $76$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(76\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(333, [\chi])\).

	Total	New	Old
Modular forms	42	18	24
Cusp forms	34	16	18
Eisenstein series	8	2	6

Trace form

\( 16 q - 22 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(333, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
333.2.c.a	$333$	$2$	333.c	37.b	$2$	$2$	$2$	$2.659$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2q^{4}-iq^{5}+3q^{7}+4q^{10}+\cdots\)
333.2.c.b	$333$	$2$	333.c	37.b	$2$	$2$	$2$	$2.659$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+2iq^{5}+3iq^{8}-2q^{10}+\cdots\)
333.2.c.c	$333$	$2$	333.c	37.b	$2$	$4$	$4$	$2.659$	4.0.27648.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}-2q^{7}+\cdots\)
333.2.c.d	$333$	$2$	333.c	37.b	$2$	$8$	$8$	$2.659$	8.0.\(\cdots\).1	\(\Q(\sqrt{-111}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{4}q^{2}+(-2+\beta _{7})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(333, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(333, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)