Space of modular forms of level 333, weight 3, and Character 333.i

• Label: 333.3.i
• Level: $333$
• Weight: $3$
• Character orbit: 333.i
• Rep. character: $\chi_{333}(154,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $114$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(114\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(333, [\chi])\).

	Total	New	Old
Modular forms	160	64	96
Cusp forms	144	60	84
Eisenstein series	16	4	12

Trace form

\( 60 q - 2 q^{2} - 14 q^{5} - 4 q^{7} + 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(333, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
333.3.i.a	$333$	$3$	333.i	37.d	$4$	$12$	$6$	$9.074$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(6\)	\(0\)	\(6\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}-\beta _{6})q^{2}+(1-\beta _{1}+\beta _{3}-3\beta _{6}+\cdots)q^{4}+\cdots\)
333.3.i.b	$333$	$3$	333.i	37.d	$4$	$24$	$12$	$9.074$		None		$2$	$0$	\(-8\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
333.3.i.c	$333$	$3$	333.i	37.d	$4$	$24$	$12$	$9.074$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(333, [\chi])\) into lower level spaces

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