Space of modular forms of level 2700, weight 2, and Character 2700.cs

• Label: 2700.2.cs
• Level: $2700$
• Weight: $2$
• Character orbit: 2700.cs
• Rep. character: $\chi_{2700}(67,\cdot)$
• Character field: $\Q(\zeta_{180})$
• Dimension: $25728$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2700.cs (of order \(180\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2700 \)
Character field:			\(\Q(\zeta_{180})\)
Sturm bound:			\(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

	Total	New	Old
Modular forms	26112	26112	0
Cusp forms	25728	25728	0
Eisenstein series	384	384	0

Trace form

25728 * q - 48 * q^2 - 60 * q^4 - 96 * q^5 - 36 * q^6 - 24 * q^8 - 120 * q^9 - 24 * q^10 - 48 * q^12 - 96 * q^13 - 60 * q^14 - 36 * q^16 - 48 * q^17 - 90 * q^18 - 48 * q^20 - 72 * q^21 - 48 * q^22 - 96 * q^25 - 192 * q^26 - 96 * q^28 - 120 * q^29 - 48 * q^30 + 12 * q^32 - 96 * q^33 - 60 * q^34 - 36 * q^36 - 48 * q^37 - 60 * q^38 - 48 * q^40 - 72 * q^41 - 288 * q^42 - 30 * q^44 - 96 * q^45 - 18 * q^46 - 48 * q^48 - 48 * q^50 - 48 * q^52 - 192 * q^53 - 60 * q^54 - 36 * q^56 - 132 * q^57 - 48 * q^58 - 288 * q^60 - 72 * q^61 - 24 * q^62 - 30 * q^64 - 48 * q^65 - 36 * q^66 - 24 * q^68 - 120 * q^69 - 48 * q^70 - 48 * q^73 - 144 * q^76 - 96 * q^77 + 174 * q^78 + 84 * q^80 - 72 * q^81 - 96 * q^82 - 60 * q^84 - 96 * q^85 - 36 * q^86 - 60 * q^89 + 120 * q^90 + 66 * q^92 + 48 * q^93 - 60 * q^94 - 36 * q^96 - 96 * q^97 - 138 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.