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 - 32 * q^10 - 22 * q^12 - 16 * q^13 - 10 * q^14 - 6 * q^16 - 64 * q^17 + 16 * q^18 + 8 * q^20 - 24 * q^21 - 16 * q^25 - 64 * q^26 - 48 * q^28 - 20 * q^29 - 6 * q^30 - 28 * q^32 - 20 * q^33 - 10 * q^34 + 4 * q^36 - 64 * q^37 + 24 * q^38 - 8 * q^40 - 12 * q^41 + 146 * q^42 - 40 * q^44 - 12 * q^45 - 24 * q^46 - 128 * q^48 - 48 * q^50 + 8 * q^52 - 16 * q^53 - 150 * q^54 - 6 * q^56 + 8 * q^57 + 106 * q^60 - 12 * q^61 - 84 * q^62 - 40 * q^64 - 32 * q^65 + 12 * q^66 - 68 * q^68 - 40 * q^69 + 12 * q^70 - 98 * q^72 - 64 * q^73 + 40 * q^77 - 74 * q^78 - 172 * q^80 - 24 * q^81 - 40 * q^82 - 20 * q^84 - 16 * q^85 - 6 * q^86 - 80 * q^89 - 158 * q^90 - 62 * q^92 + 28 * q^93 + 110 * q^94 - 12 * q^96 - 16 * q^97 - 244 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	900.2.bs.a	$8$	$0$	\(-8\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{60}]$