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

• Label: 333.2.t
• Level: $333$
• Weight: $2$
• Character orbit: 333.t
• Rep. character: $\chi_{333}(85,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(76\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	80	80	0
Cusp forms	72	72	0
Eisenstein series	8	8	0

Trace form

\( 72 q - 3 q^{2} + 35 q^{4} - 3 q^{5} - 6 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

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.t.a	$333$	$2$	333.t	333.t	$6$	$2$	$1$	$2.659$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
333.2.t.b	$333$	$2$	333.t	333.t	$6$	$4$	$2$	$2.659$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$1$	\(-3\)	\(0\)	\(-9\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1})q^{2}+(-1+2\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
333.2.t.c	$333$	$2$	333.t	333.t	$6$	$66$	$33$	$2.659$		None		$2$	$0$	\(3\)	\(3\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$