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

• Label: 333.2.br
• Level: $333$
• Weight: $2$
• Character orbit: 333.br
• Rep. character: $\chi_{333}(17,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.br (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	504	144	360
Cusp forms	408	144	264
Eisenstein series	96	0	96

Trace form

\( 144 q + O(q^{10}) \)

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.br.a	$333$	$2$	333.br	111.q	$36$	$144$	$12$	$2.659$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

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

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