Space of modular forms of level 225, weight 4, and Character 225.w

• Label: 225.4.w
• Level: $225$
• Weight: $4$
• Character orbit: 225.w
• Rep. character: $\chi_{225}(2,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1408$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(225, [\chi])\).

	Total	New	Old
Modular forms	1472	1472	0
Cusp forms	1408	1408	0
Eisenstein series	64	64	0

Trace form

\( 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(225, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.4.w.a	$225$	$4$	225.w	225.w	$60$	$1408$	$88$	$13.275$		None		$4$	$0$	\(-24\)	\(-20\)	\(-24\)	\(-8\)		$\mathrm{SU}(2)[C_{60}]$