Space of modular forms of level 225, weight 3, and Character 225.x

• Label: 225.3.x
• Level: $225$
• Weight: $3$
• Character orbit: 225.x
• Rep. character: $\chi_{225}(13,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $928$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.x (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(225, [\chi])\).

	Total	New	Old
Modular forms	992	992	0
Cusp forms	928	928	0
Eisenstein series	64	64	0

Trace form

\( 928 q - 8 q^{2} - 14 q^{3} - 10 q^{4} - 8 q^{5} - 12 q^{6} - 8 q^{7} - 16 q^{8} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(225, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.3.x.a	$225$	$3$	225.x	225.x	$60$	$928$	$58$	$6.131$		None		$4$	$0$	\(-8\)	\(-14\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{60}]$