Space of modular forms of level 900, weight 2, and Character 900.bs

• Label: 900.2.bs
• Level: $900$
• Weight: $2$
• Character orbit: 900.bs
• Rep. character: $\chi_{900}(67,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $2816$
• Newform subspaces: $1$
• Sturm bound: $360$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bs (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 900 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(360\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).

	Total	New	Old
Modular forms	2944	2944	0
Cusp forms	2816	2816	0
Eisenstein series	128	128	0

Trace form

\( 2816 q - 8 q^{2} - 10 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{8} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.2.bs.a	$900$	$2$	900.bs	900.as	$60$	$2816$	$176$	$7.187$		None		$8$	$0$	\(-8\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{60}]$