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

• Label: 333.2.s
• Level: $333$
• Weight: $2$
• Character orbit: 333.s
• Rep. character: $\chi_{333}(64,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $76$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(76\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	84	36	48
Cusp forms	68	32	36
Eisenstein series	16	4	12

Trace form

\( 32 q + 6 q^{2} + 16 q^{4} - 4 q^{7} + O(q^{10}) \)

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.s.a	$333$	$2$	333.s	37.e	$6$	$2$	$1$	$2.659$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(4-2\zeta_{6})q^{5}+\cdots\)
333.2.s.b	$333$	$2$	333.s	37.e	$6$	$4$	$2$	$2.659$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+(2-2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
333.2.s.c	$333$	$2$	333.s	37.e	$6$	$4$	$2$	$2.659$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(3\)	\(0\)	\(-3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots\)
333.2.s.d	$333$	$2$	333.s	37.e	$6$	$6$	$3$	$2.659$	6.0.16553403.1	None		$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(2-2\beta _{2}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
333.2.s.e	$333$	$2$	333.s	37.e	$6$	$8$	$4$	$2.659$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}+(-1-\beta _{3})q^{4}+\beta _{7}q^{5}+(-2+\cdots)q^{7}+\cdots\)
333.2.s.f	$333$	$2$	333.s	37.e	$6$	$8$	$4$	$2.659$	8.0.592240896.6	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{4})q^{2}+(-\beta _{1}+3\beta _{2})q^{4}+\cdots\)

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

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