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

• Label: 333.2.f
• Level: $333$
• Weight: $2$
• Character orbit: 333.f
• Rep. character: $\chi_{333}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $30$
• Newform subspaces: $4$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
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	84	34	50
Cusp forms	68	30	38
Eisenstein series	16	4	12

Trace form

\( 30 q + q^{2} - 17 q^{4} - 3 q^{5} + 2 q^{7} - 6 q^{8} + O(q^{10}) \)

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.f.a	$333$	$2$	333.f	37.c	$3$	$2$	$1$	$2.659$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
333.2.f.b	$333$	$2$	333.f	37.c	$3$	$6$	$3$	$2.659$	6.0.1415907.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\cdots\)
333.2.f.c	$333$	$2$	333.f	37.c	$3$	$10$	$5$	$2.659$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{2}-2\beta _{6}+\beta _{8})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
333.2.f.d	$333$	$2$	333.f	37.c	$3$	$12$	$6$	$2.659$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{5}+\beta _{9})q^{4}+\beta _{10}q^{5}+\cdots\)

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

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